Materials Included In Kit

Additional Materials Required

Prelab Preparation

Experiment 2: Transverse Wave Visualizer

Use a red-colored marker to completely color in the lone unshaded outlined box on each of the Line Pattern Transparencies.

Experiment 4: Resonance Tube

It may be necessary to press the foam plugs into the cardboard tubes in order to shape them properly before the students first use them. The initial fitting may be tight and if this is not performed carefully the foam plugs may break. Once the foam plugs have been inserted once, they will retain their shape and the students should be able to slide them in and out of the tubes easily and without them breaking.

Experiment 5: Singing Rods

Pour a small amount (≈ 10 g) of rosin into a weighing dish, watch glass or small beaker. Students will need only a small amount on their fingertips. Provide as little as possible to prevent the possibility of a large mess at the end of the day.

Safety Precautions

Most of the materials for this lab are considered safe. Students should wear safety glasses when working with the springs. Be sensitive to anyone who might have a hearing problem. Tuning fork vibrations might bother some individuals. Never touch fragile objects (e.g., glass, teeth) with a vibrating tuning fork. Students need to use care when handling the rosin. This fine powder can easily cause a mess. Students should be advised to wash hands with soap and water when this experiment is complete. Please follow all normal laboratory safety guidelines.

Disposal

The materials from each lab may be saved and stored in their original containers for future use.

Lab Hints

• This comprehensive Waves and Sound Kit is designed to give students the opportunity to explore the fundamentals of waves and sound. Five hands-on lab stations can be arranged so student groups can experiment with different aspects of frequency, resonance, wave properties, interference principles and the Doppler effect.

Experiment 1: Visible Waves

• Enough materials are provided in this kit for two groups of students to work at the same lab station. This laboratory activity can reasonably be completed in one 20-minute class period.
• Students can tie string to one end of the Slinky and then tie it to a table leg, doorknob or hold the Slinky by the string to obtain a “free-ended” spring. Holding both ends rigid produces a “rigid-end” spring.
• Long “Wave Demonstrator” springs (Flinn Catalog No. AP9023) can also be used for this experiment.

Experiment 2: Transverse Wave Visualizer

• Enough materials are provided in this kit for four groups of students to work at the same lab station. This laboratory activity can reasonably be completed in one 20-minute class period.
• This activity relates the frequency and wavelength of a wave to the constant speed of a wave in a media. This is the fundamental principle of all waves—electromagnetic as well as ocean waves.

Experiment 3: Simulated Double-Slit Interference

• Enough materials are provided in this kit for two groups of students to work at the same lab station. This laboratory activity can reasonably be completed in one 20-minute class period.
• One set of each circle pattern plate is provided. Student groups will need to share the plates during the experiment—one group working with Plate A while the other group experiments with Plate B. Students will need to swap one A plate for one B plate in order to answer Question 6.
• This activity teaches an advanced wave topic and may not be suitable for all students. This activity can also be performed as a demonstration using an overhead projector to show students the interference pattern without doing any calculations.
• The Background section and physical science textbooks should be used by students to better understand the principles of interference.
• The “wavelength” of the plate point sources and the point source separation are much larger than wavelengths of visible light. However, this is still an excellent simulation of the interference of coherent light because the ratios between the wavelength and point source separation will be the same. Red laser light has a wavelength of approximately 645 nm. The double-slit separation needed for the first order bright band to occur at 15° is approximately 2490 nm. For the simulated interference experiment, with a point source wavelength of 3.5 mm, the double-slit separation needs to be 13.5 mm for the first order bright band to occur at 15°. The ratio of 645 nm : 2490 nm is the same as the ratio of 3.5 mm : 13.5 mm—equal to 0.26.

Experiment 4: Resonance Tube

• Enough materials are provided in this kit for two groups of students to work at the same lab station. This laboratory activity can reasonably be completed in one 30-minute class period.
• Only one of each tuning fork is provided. The student groups need to share the 426-Hz and 512-Hz tuning forks as they work on this experiment.
• Provide students with rulers that do not have “dead space” at the end. The rulers should begin at zero at the edge of the ruler.
• The sliding resonance tube activities can be conducted as just “listening” labs or they can be quantified with calculations. Consider course goals and student experience when contemplating the teaching strategy for this laboratory.
• Relate the results of this lab to actual musical instruments. Bring clarinets, saxophones or trumpets to class and relate column length to resonance.
• The end corrections are small for these resonance tubes. The “true” wavelength for this tube is two times the length of the tube at resonance plus an additional correction of 3.8 cm for the difference in the size of the two ends. Therefore, the actual lengths of the resonating tubes will be slightly smaller than those calculated in the Prelab Preparation. This information may be provided to students as they perform their calculations.
• The resonating tube length calculations are also based on the assumption that the speed of sound is 343 m/s. This value will vary with temperature and humidity.

Experiment 5: Singing Rods

• Enough materials are provided in this kit for one student group. It may be difficult for two groups to work together with this experiment because too many singing rods could make it difficult to interpret the sounds and may be distracting to other groups. This laboratory activity can reasonably be completed in one 20-minute class period.
• The rosin may come in the form of a bag or in a bottle. If the rosin comes in a bag (a baseball pouch), remove the paper from the cloth bag and then place the cloth bag full of rosin back into the zipper-lock bag. The porous cloth bag can create a mess if not kept inside a secondary container.
• Whether the rosin comes in a bag or a bottle, it is recommended that a small amount of rosin is placed on a watch glass or weighing dish for student use. Students only need a small amount of rosin on their fingertips to produce a “singing rod.”
• Remind students that they only need a small amount of rosin on their fingertips. They should clean up rosin spills with a paper towel.
• Wearing disposable latex gloves can also be used in place of coating fingers in rosin. The friction from the gloves will cause the rods to “sing.”
• Use computer- or calculator-based technology equipment or an oscilloscope with a microphone to measure and observe the sound frequencies produced by the resonating Singing Rod. Compare the wave patterns to those predicted.

Teacher Tips

• Set up each lab station accordingly before class. Students should leave the stations as they find them before they move on to the next lab station.
• Before class, prepare copies of the student worksheets for each student. The Background section for each experiment can also be copied at the instructor’s discretion.

Answers to Prelab Questions

Experiment 4: Resonance Tube

1. Calculate the length of an open-open resonance tube that resonates the fundamental frequency of a 512-Hz tuning fork. Repeat the calculation for a 426-Hz tuning fork. Assume the speed of sound is 343 m/s.

   512-Hz Tuning Fork:
   Wavelength = Velocity/Frequency = (343 m/s)/512 Hz = 0.67 m
   
   426-Hz Tuning Fork:
   Wavelength = Velocity/Frequency = (343 m/s)/426 Hz = 0.81 m
   
   Length for the Fundamental Wavelength:
   Length = Wavelength/2 = 0.67 m/2 = 0.335 m = 34 cm (512-Hz)
   = 41 cm (426-Hz)

2. Calculate the length of a closed-open resonance tube that resonates the fundamental frequency of a 512-Hz tuning fork. Repeat the calculation for a 426-Hz tuning fork. Assume the speed of sound is 343 m/s.

   Length for the Fundamental Wavelength:
   Length = Wavelength/4 = 0.67 m/4 = 0.168 m = 17 cm (512-Hz)
   = 20 cm (426-Hz)

Sample Data

Experiment 1: Visible Waves

Transverse Wave

Describe the wave motion.

The wave pulse travels with a constant speed from start to finish. After the pulse moves past a certain part of the spring, the spring comes to rest and the parts of the spring in the direction of propagation move up. The height of the wave pulse remains about the same for the entire motion.

Does the size of the transverse wave pulse change as it travels along the spring?

No, the size of the wave pulse remains about the same the whole time. It gets a little smaller as it flips over and travels back toward the start.

What happens to the wave as the spring is stretched further?

As the spring is stretched further, the wave pulse travels faster. The wave pulse has a smaller height compared to when the spring is stretched less.

What happens to the wave when it reaches the end of the spring?

The wave pulse flips over and is reflected back toward the starting end of the spring. The height of the wave pulse is slightly smaller than the original wave.

Longitudinal Waves

Describe the wave (pulse) motion.

The wave pulse continuously compresses and relaxes the spring as it propagates down the spring. The compressed region of spring moves away from where the pulse started. It is more difficult to determine the “height” of the wave, except by the darkness of the compressed regions of the spring. The darker the regions, the more compressed the spring and therefore the larger the “height.”

Does the size of the longitudinal wave change as it travels along the spring?

The longitudinal wave changes more than the transverse wave as it moves down the spring. At the end of the spring, the wave pulse is no longer as compressed as it initially starts and appears “weaker.”

What happens to the wave as the spring is stretched further?

The speed of the wave pulse increases as the spring is stretched further.

What happens to the wave (pulse) when it reaches the end of the spring?

The wave pulse is reflected back to the source. The pulse is much weaker than before, but it appears to be traveling with the same speed.

Experiment 3: Simulated Double-Slit Interference Experiment 4: Resonance Tube Experiment 5: Singing Rods

Observations—Part I. Singing Rods

Aluminum rod, thick, 24"

The ends of the humming aluminum rod vibrate very quickly initially, but then the motion appears to stop while the humming is still present. When the ends are touched, the sound stops. When the humming is louder, the initial vibrations are larger, but the vibrations always appear to stop even when the aluminum rod continues to “sing.”

It is difficult to get the aluminum rod to resonate at other points along the rod. When held at about one-quarter length, the aluminum rod resonated with a higher-pitched sound. (The aluminum rod will also resonate when held at the 1/6th length.)

Aluminum rod, thin 24"

This rod also began to hum with a very similar pitch to the thicker rod. The sound did not last as long as the thicker rod. It too resonated when held at one-quarter of its length, and it hummed with a higher pitch at this holding position.

Aluminum tube, 24"

The tube again hummed with a similar pitch to the thick and thin rod. It appeared to be louder, but had the same sound. It did not appear to matter that it was a tube instead of a solid rod.

Aluminum rod, thick, 18"

The shorter aluminum rod produced a higher-pitched sound than the longer rods and tube. It was harder to resonate the shorter rod compared to the longer ones. A very high-pitched sound was heard when it was held at the one-quarter position.

Observations—Part II. Doppler Effect

When the “singing rod” end moves away, the sound produced by the Singing Rod appears to drop to a lower pitch. When it moves closer, the pitch appears to increase. The faster the rod is rotated, the lower and higher the pitch sounds.

Answers to Questions

Experiment 2: Transverse Wave Visualizer

1. How do the speeds of the wave fronts (red line) compare?

   The wave speeds are exactly the same for each wave front.

2. Is the transverse (up and down) motion of the red mark the same for each wave?

   The transverse motion is different for each wave. For the longer wavelength, the motion of the red mark is slow. For the shortest wavelength, the red mark moves up and down three times as much as the longest wavelength for the same distance traveled.

3. What is the relationship between the wavelength and the transverse motion of the red mark (frequency)?

   The relationship between wavelength and frequency is opposite (inverse). When the wavelength is long, the frequency (the number of transverse motions) is low. When the wavelength is short, the frequency is high.

Experiment 3: Simulated Double-Slit Interference

1. Calculate the “wavelength” of the point source for Pattern A using the first-order data.

   Using Equation 1, the wavelength will be:
   First order: sin 40° = (1) x λ/(5 mm) → λ = 3.2 mm

2. Calculate the “wavelength” of the point source for Pattern A using the second-order data.

   Using Equation 1, the wavelength using second order data is:
   Second order: sin 26° = (2) x λ/(15 mm) → λ = 3.3 mm

3. Calculate the position of the first-order maximum for Pattern B using one of the slit separations chosen during the lab.

   The first-order bright band for slit separation of 1.0 mm will be located at:
   First order: sin θ = (1) x (5 mm)/(15 mm) → θ = 19°

4. Calculate the position of the second-order maximum for Pattern B using the same slit separation chosen in Question 3.

   The second-order bright band for slit separation of 1.0 mm will be located at:
   Second order: sin θ = (2) x (5 mm)/(15 mm) → θ = 42°

5. Radio signals (approximately 3 m wavelengths) have the ability to “bend” around buildings so that a radio station can be heard throughout a city. In contrast, visible light waves (approximately 500 nm wavelengths) do not bend around buildings (the building casts a shadow). Why would electromagnetic radio signals bend (diffract) around buildings better than visible light? Hint: Refer to Equation 1.

   Buildings are typically about 50 m wide. This would be the approximate slit separation. A 3-m wave is “bent” more than a 500-nm wave by such a large slit (object).

6. Was an interference pattern created when Pattern A and Pattern B were used together? Explain.

   No, an interference pattern did not develop when Patterns A and B were stacked on top of each other and moved around. In order for interference patterns to develop, monochromatic sources (sources with the same wavelength) must be used. Wave patterns of different wavelengths do not interfere with each other, in general.

Experiment 4: Resonance Tube

1. How long is the fundamental wavelength of the sound resonating in the open-open resonance tube?

   The fundamental wavelength of sound resonating in an open-open resonance tube is twice the length of the tube.

2. How long is the fundamental wavelength of the sound resonating in an open-closed resonance tube?

   The fundamental wavelength of sound resonating in an open-closed resonance tube is four times the length of the tube.

3. Calculate the speed of sound in air using the data from the open-open resonance tube.

   Velocity = Frequency x Wavelength = 512 Hz x (2 x 0.289 m) = 296 m/s

4. Calculate the speed of sound in air using the data from the closed-open resonance tube.

   Velocity = Frequency x Wavelength = 512 Hz x (4 x 0.152 m) = 311 m/s

5. How do the lengths of the resonating tubes and the speed of sound calculations compare to the calculations and given value in the Prelab Questions? What factors could attribute to any variations?

   The lengths of the resonating tubes were a few centimeters shorter than the lengths predicted in the Prelab calculations. The speed of sound calculation was low by more than 30 m/s. The error in the initial calculation could have been caused by the assumption that the speed of sound in air is 343 m/s. The speed of sound is dependent on the air temperature and humidity, and 343 m/s is the speed of sound at 20 °C. Also, the tuning forks may not be precisely calibrated to the labeled frequency. The diameter of the tube may also contribute to some error in the resonance. A thinner tube may resonate more closely to the predicted value.

Experiment 5: Singing Rods

1. Why do the aluminum rods resonate and “sing” when they are rubbed with the rosin? What is the purpose for the rosin?

   The aluminum rod begins to resonate because the rod is relatively uniform and the material has a natural vibration frequency. Rubbing with the rosin helps generate vibrations in the rod which tend to vibrate in one of the natural resonance frequencies of the metal rod. Holding the rod in the middle allows fundamental harmonic frequency to resonate predominately. Holding the rod at one-quarter length also produced resonance. Holding it at the end did not produce any resonance (or vibration of any kind). The rosin increases the friction between the fingers and the rod which helps to increase the vibrations in the rod as the fingers stroke it.

2. At what point on the aluminum rod does the sound appear to be produced?

   The sound appears to be “emitted” from the ends of the rod.

3. Why must the aluminum rod be held in the middle in order for resonance to occur? Are there any other positions where the aluminum rod can be held that produces resonance?

   The middle of the aluminum rod represents a node for the resonating frequencies of the metal rod. A node is a place where no vibration occurs in a standing wave. So, holding at a node will not affect the vibrations. Holding the aluminum rod at an antinode (maximum amplitude) position will prevent the rod from resonating. Another node occurs at the one-quarter position for the 3rd harmonic and one-sixth position for the 5th harmonic.

4. Compare the sounds produced by the four “singing rods.”

   The sounds produced by the two rods and one tube that were the same length were very similar in pitch. The thin rod did not resonate very long, and the tube appeared to produce a louder sound. The shorter rod produced a higher pitch than the other three.

5. Define the Doppler effect.

   See Background information.

6. Explain why the sound of the “singing rod” changes when the rod is rotated forward and back.

   As the vibrating rod moves forward, toward an individual, the sound wave “point sources” move with the rod and the sound waves get “bunched together.” This makes the sound appear to have a higher frequency than the original stationary sound. When the rod moves away, the “point sources” are spread further apart and the sound waves are spaced further apart than the original wave and the sound appears to have a lower frequency. The faster the rod is rotated, the larger the apparent change in frequency to the higher and lower range.

Introduction

This comprehensive Waves and Sound Kit is designed to provide the opportunity to explore the fundamentals of waves and sound. Five hands-on lab stations allow experimentation with different aspects of frequency, resonance, wave properties, interference principles and the Doppler effect.

Concepts

• Transverse waves
• Frequency
• Rarefaction
• Longitudinal waves
• Amplitude
• Compression
• Wavelength
• Speed of light
• Interference pattern
• Coherent light
• Diffraction
• Resonance
• Sine wave
• Antinode
• Node
• Harmonics
• Doppler effect

Background

Experiment 1: Visible Waves

What are waves? A wave is a displacement or disturbance (vibration) that moves through a medium or space. A wave involves the movement of energy or a disturbance that changes in magnitude with respect to time at a given location and changes in magnitude from place to place at a given time. Waves can move through materials such as springs, air and water. Two basic wave types (transverse and longitudinal) are usually demonstrated with a wave demonstration spring. Transverse waves displace particles perpendicular to the direction of the wave propagation. Longitudinal waves displace particles parallel to the direction of the propagation (see Figure 1).

Waves display characteristic properties of wavelength, amplitude and frequency. Figure 2 shows a representation of some of these characteristics. Experiment 2: Transverse Wave Visualizer

All electromagnetic radiation travels at the same constant speed through a vacuum. This constant speed is known as the speed of light and is designated with the symbol c, where c = 2.998 x 10⁸ m/s in a vacuum. Experiments have shown that electromagnetic radiation travels in a similar fashion to that of water waves in a ripple tank or pond—that is, electromagnetic radiation travels in the form of waves, more specifically transverse waves. A transverse wave is described as a wave in which the disturbance of the wave pattern travels at a right angle to the direction of motion of the wave. Conversely, for a longitudinal wave (also known as a compression wave), the wave pattern disturbance travels along the same direction as the direction of motion of the wave. Sound waves are examples of longitudinal waves (see Figure 3). Reminiscent of all waves, electromagnetic waves have a wavelength, frequency, speed and an amplitude (see Figure 4). The frequency of the wave is a measure of how quickly the wave repeats itself and is measured in Hertz. The relationship between the wavelength and the frequency of a wave is determined by the speed of the wave (the speed of light for electromagnetic waves) according to the following equation.

c = λν

c = speed of light (speed of the wave)
λ = wavelength of the wave (Greek letter lambda)
ν = frequency of the wave (Greek letter nu)

Since c is a constant, it can be seen from the equation that as electromagnetic radiation wavelength decreases, the frequency must increase. This relationship between frequency and wavelength is called an inverse relationship.

This activity illustrates this inverse relationship between the frequency and the wavelength for waves that travel at the same speed. The three wave patterns (A, B and C) have three different wavelengths, 1½", 3" and 4½", respectively. The red mark in each wave image represents the wave front (the leading edge of the wave). As the line pattern is moved over the wave patterns, the red mark travels at the same lengthwise speed which shows that the three wave fronts are traveling at the same speed. By observing the red mark in each wave pattern, it can be seen that the red mark in the shorter wavelength wave, A, “travels” up and down much more frequently than for the longer wavelength patterns (B and C). The transverse motion is quicker for the shorter wavelength wave—it has a higher frequency. More specifically, every time the red mark travels an entire wavelength in the longer wavelength wave (C), the red mark travels up and down a total of three times in the shortest wavelength wave (A). Wave A’s wavelength is three times shorter than wave C’s wavelength, and therefore the frequency of A must be three times faster than C because the waves are traveling at the same speed.

Experiment 3: Simulated Double-Slit Interference

Interference of light occurs when light travels through thin slits that are very close together. The light exiting the thin slit spreads out at a wide angle as if the light originated from the slit as a point source (see Figure 5). This phenomenon is known as diffraction. Interference and diffraction explain how certain waves, such as radio waves, can “bend” around solid objects such as buildings. The buildings act like “slits” for the radio waves, resulting in many “point sources” broadcasting the original radio signal.

If all the light is the same wavelength and phase, also known as coherent light, then an interference pattern will develop. Laser light is an example of coherent light. An interference pattern develops because the coherent light has to travel different distances to reach the same point. If the path lengths are just right, two light waves will reach the same point “in phase” and result in constructive interference, generating a bright spot of light. Destructive interference occurs when the light waves are “out of phase” as they reach the same point, resulting in the creation of a dark band (see Figure 6). The location of the bright bands obtained when coherent light passes through a diffraction grating can be predicted using Equation 1. Equation 1 relates the angle of the bright bands to the wavelength of the light source and the slit separation. This equation can also be used for double-slit interference.

λ = wavelength of light
d = slit separation (point source separation)
θ = angle of the bright band from the normal
m = order of the band

Experiment 4: Resonance Tube

Many musical instruments work because air is vibrated in an air column and then the length of the air column is varied to change the sound produced. The length of the air column determines the pitch of the sound of the vibrating air. A mixture of different frequencies and the resonation of air columns on a particular set of frequencies can turn noise into music. Changing the length of the column of vibrating air can vary the pitch of the musical instrument. The sound produced is the loudest when the air column is in resonance (in tune) with the vibrational source.

How does resonance occur? A vibrating source produces a sound wave. This wave consists of alternating high- and low-pressure variations as it moves through an air column. Sound waves are often depicted as a sine wave as shown in Figure 1. The sound wave is ultimately reflected back toward the vibrational source. It is either reflected back off a closed end of the column or as a low-pressure reflection off the open end of the column. If the reflected wave reaches the vibrational source at the same moment another wave is produced, then the leaving and returning waves reinforce each other. This reinforcement, called resonance, is achieved and a standing wave is produced. A standing wave is a wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere with each other. A node is a point in a standing wave that always undergoes complete destructive interference and therefore is stationary. An antinode is a point in the standing wave, halfway between two nodes, at which the largest amplitude occurs. To determine when and where resonance will occur, the speed (v), frequency (f) and wavelength (λ) must be determined. (Note: Frequency is also referred to using the Greek symbol ν.) All three are related by the following equation: Standing waves have been characterized based upon a fundamental frequency and are a part of what is known as the harmonic series (see Figure 8). Most waves need a medium to propagate through—such as water or air. In this experiment, investigate waves that resonate in solid metal, and use the vibrating metal to experience the Doppler effect. The fundamental frequency (f₁) corresponds to the first harmonic, the next frequency (f₂) corresponds to the second harmonic, and so on. Because each harmonic is an integral multiple of the fundamental frequency, the equation for the fundamental frequency can be generalized to include the entire harmonic series. Thus f_n = nf₁ where f₁ is the fundamental frequency (f₁ = v/2L) and f_n is the frequency of the nth harmonic.

A standing wave in a column can be represented by a sine wave in either an open-open or a closed-open column. The shortest column of air that can have nodes at both ends in an open-open column is one-half wavelength long as shown by f₁ in Figure 9. Note: Figures 9 and 10 represent standing pressure waves. The node is at a place of low pressure and the antinode is at high pressure. Standing air displacement waves are represented by the dashed line in f₁ of Figures 9 and 10. An open-open column resonates when its length is an even number of quarter wavelengths (e.g., 2, 4, 6). As the frequency is increased, additional resonance lengths are found at half-wavelength intervals. Thus, columns of length λ/2, λ, 3λ/2, 2λ and so on will be in resonance for an open-open tube. The shortest column of air that can have an antinode at the closed end of a closed-open column and a node at the open end is one-quarter wavelength as shown by f₁ in Figure 10. A closed-open column resonates when its length is an odd number of quarter wavelengths (e.g., 1, 3, 5). As the frequency is increased, additional wavelengths are found at half-wavelength intervals. If open-open and closed-open columns of the same length are used as resonators, the wavelength of the resonant sound for the open pipe will be one-half as long as in the closed-open pipe. Therefore, the frequency will be twice as high for the open column as for the closed column. For both columns, resonance lengths are spaced by half-wavelength intervals.

Experiment 5: Singing Rods

All sounds originate from a vibrating object. A vibration is simply a rapid wiggling of an object. The rapid back-and-forth motion of a tuning fork is a familiar example of a vibration. When an object vibrates it causes the air molecules surrounding the object to move. The rapidly vibrating object compresses the air molecules together briefly, and when the object moves away from the air molecules, a less pressurized, low-density air pocket is created. This region of lower density and pressure is referred to as rarefaction.

The aluminum rod vibrates when it is tapped by an external source. If the aluminum rod is held at a node for a specific harmonic frequency, standing waves can be produced if the vibrations continue. Stroking the aluminum rod with rosin creates vibrations in the rod due to the “stick-slip” nature of the rosin. These vibrations build on each other to create standing waves that resonate the rod at a particular harmonic wavelength. If the rod is of the proper length, this vibrating wave will produce a sound wave that can be heard. Standing waves have nodes (regions of no displacement) and antinodes (regions of greatest displacement). The wave pattern that develops in an aluminum rod is known as a longitudinal wave—similar to the waves that develop in air. For longitudinal waves, compression and rarefaction are produced. These motions are so small in the aluminum rod that they may not even be noticed. Transverse waves can also be seen initially in the “singing rod” as the ends vibrate back and forth. However, it is the longitudinal waves that resonate in the metal rod and generate the sound that is heard. This explains why the “singing rod” resonates louder the more times it is stroked. If transverse waves were supposed to resonate, the rubbing action down the length of the aluminum rod would dampen out these types of vibrations. Instead, the aluminum rod gets louder and louder, indicating that longitudinal standing waves are being produced.

The aluminum rod will resonate when it is held in the middle, one-quarter length and one-sixth length. This represents the first, third and fifth harmonics of the rod. It would seem logical that the second and fourth harmonics should also resonate, but the rigidness of the rod limits the mid-point of the metal bar from acting as an antinode. The “singing rod” works best when the mid-point is a node (see Figure 11). The Doppler effect occurs when there is a frequency shift due to the relative motion between the source of a wave pattern and an observer. If a sound source of known frequency travels in a straight line toward one individual and away from a second individual, both individuals will hear a sound of a frequency different from the “known” source frequency (see Figure 12). The individual in front of the moving source will receive the sound waves more frequently than they are actually produced by the sound source. Therefore, the sound that this individual hears will have a higher pitch than what is actually being emitted by the sound source. The individual that observes the sound source moving away will receive the sound waves less frequently than they are actually produced by the source. This observer will hear a lower pitch compared to the actual pitch of the sound source. An observer traveling at the same speed and direction as the sound source will hear the true frequency of the sound because there will be no relative motion between the source and the observer. As the “singing rod” rotates toward an individual, the pitch will increase. As the end of the “singing rod” moves away, the pitch will decrease.

Experiment Overview

Visible Waves

Use a coiled spring to visualize the two wave types and compare their properties.

Transverse Wave Visualizer

How are wavelength and frequency related in a transverse wave? This activity allows you to visualize the relationship between wavelength and frequency.

Simulated Double-Slit Interference

Diffraction and interference are properties of light that are not commonly observed in everyday life. Light we see is composed of different wavelengths, intensities, polarization and phases. A coherent light source, or light composed of a single wavelength, such as laser light, and a diffraction grating or multiple-slit grating, are typically needed in order to see interference and diffraction. In this activity, double-slit interference patterns are simulated using two coherent, point-source plates.

Resonance Tube

Slide that trombone—change the length of the column of resonating air and the sound changes. Do it skillfully and the resonating noise is turned into music!

Singing Rods

Most waves need a medium to propagate through—such as water or air. In this experiment, investigate waves that resonate in solid metal, and use the vibrating metal to experience the Doppler effect.

Materials

Prelab Questions

Experiment 4: Resonance Tube

1. Calculate the length of an open-open resonance tube that resonates the fundamental frequency of a 512-Hz tuning fork. Repeat the calculation for a 426-Hz tuning fork. Assume the speed of sound is 343 m/s.
2. Calculate the length of an closed-open resonance tube that resonates the fundamental frequency of a 512-Hz tuning fork. Repeat the calculation for a 426-Hz tuning fork. Assume the speed of sound is 343 m/s.

Safety Precautions

The materials in this lab are considered safe. Take care not to suddenly release a stretched Slinky^®. The spring may snap back rapidly, which may cause personal injury or damage to the Slinky. Wear safety glasses. Do not extend the Slinky more than 3 meters. Be sensitive to anyone who might have a hearing problem. Tuning fork vibrations might bother some individuals. Never touch fragile objects (e.g., glass, teeth) with a vibrating tuning fork. Use care when handling the rosin. This fine powder can easily cause a mess. Wash hands thoroughly with soap and water before leaving the laboratory. Please follow all laboratory safety guidelines.

Procedure

Experiment 1: Visible Waves

Transverse Waves 

1. Fasten one end of the wave spring to an object (e.g., wall, table leg) with string or have a partner hold one end of the spring firmly. Hold the spring on the floor or tabletop.
2. Shake the free end of the spring up and down once. Observe the pulse move down the spring. Notice that the amplitude of the wave decreases as it moves the length of the spring.
3. Generate a train of transverse waves by shaking the spring up and down while keeping the amplitude the same.
4. Increase the frequency by shaking the spring more rapidly while keeping the amplitude the same. Shake the spring at various amplitudes keeping the frequency the same in each case.
5. Repeat trials until all the desired properties have been observed.

Longitudinal Waves 

1. Grasp one end of the spring while a partner grasps the other end.
2. Produce a longitudinal wave by quickly pushing the end of the spring forward and then pulling it backward. Observe the single series of compressions moving down the spring.
3. Produce a train of waves by repeatedly moving the end rhythmically forward and backward. The waves should travel along the spring in a series of compressions (coils closer together) and rarefactions (coils further apart).
4. Practice your technique for sending compressions down the length of the spring. The wavelength of a longitudinal wave is the distance between the compressions.
5. How can changes in the frequency be produced?
6. Repeat compressions until all the desired properties have been observed.
7. Answer all the questions in the Visible Waves Worksheet.

Experiment 2: Transverse Wave Visualizer

1. Place the Line Pattern Transparency over the Wave Pattern Transparency so that the black lines on the Line Pattern Transparency are vertical (see Figure 13).
   {13473_Procedure_Figure_13}
2. Start with the red line on the Line Pattern Transparency at one end of the Wave Pattern Transparency and then slowly slide the Line Pattern Transparency lengthwise across the Wave Pattern Transparency. The lines on the Line Pattern Transparency should be aligned perpendicular to the motion of the sheet.
3. Observe the motion of the black marks in the wave pattern images. Use the red mark in the wave patterns as a reference mark to represent the wave front of the three waves.

Experiment 3: Simulated Double-Slit Interference

1. Overlap both Concentric Circle Plate As so the circles line up evenly (see Figure 14).
   {13473_Procedure_Figure_14}
2. Slowly pull the two plates in opposite directions (one plate to the left and the other to the right). The pattern will resemble the pattern in Figure 15.
   {13473_Procedure_Figure_15}
3. Obtain the Transparency Protractor Sheet. Tape the edges of the transparency sheet to secure it to the tabletop.
4. Line up the center line on the top plate with the first dashed line on the bottom plate. Make sure the two plates are square and the “point sources” are lined up horizontally. The “zero order bright bands” should be perpendicular to the point source separation (see Figure 15).
5. Use a ruler to measure the point source separation (the horizontal distance between the center points of the top and bottom plate.) Record this value in the Simulated Double-Slit Interference Worksheet.
6. Carefully place the overlapping plates on top of the protractor transparency so that the midpoint between the point sources lines up with the center of the protractor, the point sources run along the zero line, and the zero order bright bands are bisected by the 90° lines on the protractor sheet (see Figure 16).
   {13473_Procedure_Figure_16}
7. Measure the angle that bisects the first bright band (first order) (see Figure 16). Record this angle in the Simulated Double-Slit Interference Worksheet. Note: Angles are measured relative to the perpendicular (normal), 90° angle of the zero-order bright band. For the example shown in Figure 16, the bisecting angle of the first-order bright band is 30° (90° – 60°).
8. If a second-order bright band is present, measure the angle that bisects the second bright band. Record this angle in the Simulated Double-Slit Interference Worksheet.
9. Repeat step 4, but line up the center line on one of the transparency sheets with a different dashed line on the second sheet.
10. Repeat steps 5–8.
11. Measure the “wavelength” of the coherent light source to verify the calculated “wavelength.” The wavelength is equal to the distance between the beginning of one dark circle to the beginning of the next dark circle on the concentric circle plate (e.g., 3.5 mm in this example) (see Figure 17).
    {13473_Procedure_Figure_17}
12. Repeat steps 1–11 using the B Concentric Circle Plates.
13. Place Plate A and Plate B together and skew the centers of the two patterns. Answer Question 6 on the worksheet.

Experiment 4: Resonance Tube

Open-Open Column

1. Work with a lab partner. One person should hold the tube apparatus while the other uses the tuning fork.
2. Slide the shorter cardboard tube inside the longer tube. Allow it to protrude from the tube enough to grasp the end (see Figure 18).
   {13473_Procedure_Figure_18}
3. Set the rubber pad on the table. Strike the tuning fork firmly on the rubber pad.
4. Quickly place the tuning fork near the end of the tube while sliding the tubes inside each other varying the total length of the open-open column.
5. Listen carefully and repeat the process until a tube position is located where the resonating sound is the loudest. (Note how varying the length affects the sound.)
6. Measure the length of the extended tube at the point with the greatest resonance (loudest sound). Record this value in the Resonance Tube Worksheet.
7. Repeat steps 1–6 with the other tuning fork.

Closed-Open Column

1. Use only the large diameter tube for this experiment. Carefully and slowly insert the foam plug into one end of the larger diameter tube.
2. With the short tube, or your thumb, carefully push the foam plug into one end of the large tube until the distance inside the tube is the length calculated in Prelab Question 2. Work slowly so the foam plug is not damaged and is not pushed too far into the tube. (Remove the short tube once the proper plug position is reached; see Figure 19)
   {13473_Procedure_Figure_19}
3. Strike the tuning fork and hold it at the end opposite the foam plug. Listen for loud resonance like the resonating sound produced by the open-open tube.
4. If resonance is not heard, use the short tube (or a thumb) to slide the foam plug into the tube a few millimeters. Check for resonance with the tuning fork.
5. Repeat step 4 until loud resonance is heard. Work slowly and move the foam plug only a few millimeters at a time so that the resonance distance is not missed.
6. Repeat steps 1–5 several times until you are certain about the resonance tube is resonating at its maximum.
7. Use a ruler to measure distance between the open end of the tube and the position of the foam plug. Record this distance in the Resonance Tube Worksheet. Note: Some rulers have “dead” space at the end. Use a ruler that starts at zero.
8. Use the ruler or other long object to carefully push the foam plug out of the tube. Gently push the foam plug out so that it does not break or crack.
9. Repeat steps 1–7 with the other tuning fork.
10. After completing the experiment, use the ruler or other long object to carefully push the foam plug out of the tube so that it is ready for the next lab group. Gently push the foam plug out so that it does not break or crack.

Experiment 5: Singing Rods

Part I.

1. Obtain the three aluminum rods, aluminum tube and a small amount of rosin.
2. Begin with the long, thick aluminum rod.
3. Pinch a small amount of rosin between your thumb and index finger.
4. Hold the aluminum rod vertical and at its mid-point (see Figure 20).
   {13473_Procedure_Figure_20}
5. Lightly bang the end of the aluminum rod on the tabletop to initiate a small vibration. There should be a soft humming or buzzing sound.
6. As the rod hums, pinch the middle of the rod with your rosined finger and thumb and slide your fingers down the rod. Adjust the pinch firmness accordingly to allow your hand to slide down the rod smoothly.
7. Repeat step 6 three or four times until the rod begins to hum loudly. Be sure to pinch firmly as you slide your fingers down the rod, and hold the rod at its midpoint with your other hand. Caution: Do not allow the aluminum rod to “sing” so loudly that it disrupts other lab groups.
8. When the “singing rod” stops humming or gets too quiet, repeat steps 3–7 as often as necessary to complete the observations.
9. As the aluminum rod “sings,” observe the motion at the ends of the rod. Record any observations in the worksheet.
10. Hold the aluminum rod at different locations and attempt to resonate it. Are there any other holding locations that allowed the aluminum rod to resonate? Record your observations in the worksheet.
11. Repeat steps 1–10 for the three remaining “singing rods.” (Each student in the group should resonate at least one of the “singing rods.”) Compare the tone of each singing rod. Are there different locations where these aluminum rods and tube can be held and still make them resonate? Record all your observations in the worksheet.

Part II.

12. Obtain the thick, 24" aluminum rod and a small amount of rosin.
13. Repeat steps 3–7 with the thick, long aluminum rod.
14. As the rod “sings,” hold it vertically and rotate (twirl) the top end away from you and then toward you several times. Does the sound change? How? Record your observations in the worksheet.
15. Rotate the Singing Rod faster. How does the sound change now? Record your observations in the worksheet.

Student Worksheet PDF

13473_Student1.pdf