Materials Included In Kit

Additional Materials Required

Prelab Preparation

Place the two wood blocks together and securely tape together the short ends of the blocks to form a hinge.

Safety Precautions

Use caution when clapping the wood blocks together so fingers will not get pinched. Wipe up any water spills immediately. Please follow all laboratory safety guidelines.

Disposal

The water in the tube setup may be placed down the drain. All materials may be dried and saved for future use.

Lab Hints

• This laboratory activity can be completed in two 50-minute class periods. It is important to allow time between the Introductory Activity and the Guided-Inquiry Activity for students to discuss and design the guided-inquiry procedures. Also, all student-designed procedures must be approved for safety before students are allowed to implement them in the lab. Prelab Questions may be completed before lab begins the first day.
• In order for the human ear to perceive an echo, the time lapse must be greater than 0.1 second. Otherwise a reverberation is heard. The greater the distance from the reflecting surface, the easier it is to time the claps. However, the echo will be fainter with greater distance.
• If the Introductory Activity is not feasible due to lack of ideal conditions, the echo method may also be conducted by other means. Use a computer interface system such as Vernier LabQuest™ (Flinn Catalog No. TC1561) with a microphone (Flinn Catalog No. TC2322) to record the initial sound and its echo. An online program, Audacity, is available for free download at audacity.sourceforge.net (accessed June 2014). The precision timing of either of these options allows for a much shorter distance between the sound origin and the echo.
• You may need to model the proper way to strike a tuning fork with an activator or a rubber mallet.
• If time permits, the tuning forks may be rotated among the student groups. Otherwise, each group may use a different tuning fork and share the data.

Teacher Tips

• A systematic error in the Guided-Inquiry Activity is the antinode of the standing wave at the open end of the air column is not exactly at the tube opening, but just beyond the end of the tube. The actual length differs from the measured length by a factor of 0.6 times the inner diameter of the tube. Factoring in this “end correction” is an option.

Further Extensions

Opportunities for Inquiry
Design and create a musical instrument with a range of at least one octave that can play a simple tune.

Alignment to Curriculum Framework for AP^® Physics 1

Enduring Understandings and Essential Knowledge
A periodic wave is one that repeats as a function of both time and position and can be described by its amplitude, frequency, wavelength, speed, and energy. (6B)
6B2: For a periodic wave, the wavelength is the repeat distance of the wave.
6B4: For a periodic wave, wavelength is the ratio of speed over frequency.

Interference and superposition lead to standing waves and beats. (6D)
6D3: Standing waves are the result of the addition of incident and reflected waves that are confined to a region and have nodes and antinodes. Examples should include waves on a fixed length of string, and sound waves in both closed and open tubes.
6D4: The possible wavelengths of a standing wave are determined by the size of the region to which it is confined.

Learning Objectives
6B4.1: The student is able to design an experiment to determine the relationship between periodic wave speed, wavelength, and frequency and relate these concepts to everyday examples.
6D3.1: The student is able to refine a scientific question related to standing waves and design a detailed plan for the experiment that can be conducted to examine the phenomenon qualitatively or quantitatively.
6D3.2: The student is able to predict properties of standing waves that result from the addition of incident and reflected waves that are confined to a region and have nodes and antinodes.
6D3.3: The student is able to plan data collection strategies, predict the outcome based on the relationship under test, perform data analysis, evaluate evidence compared to the prediction, explain any discrepancy and, if necessary, revise the relationship among variables responsible for establishing standing waves on a string or in a column of air.
6D4.2: The student is able to calculate wavelengths and frequencies (if given wave speed) of standing waves based on boundary conditions and length of region within which the wave is confined, and calculate numerical values of wavelengths and frequencies. Examples should include musical instruments.

Science Practices
3.2 The student can refine scientific questions.
4.1 The student can justify the selection of the kind of data needed to answer a particular scientific question.
4.2 The student can design a plan for collecting data to answer a particular scientific question.
5.1 The student can analyze data to identify patterns or relationships.
5.3 The student can evaluate the evidence provided by data sets in relation to a particular scientific question.
6.4 The student can make claims and predictions about natural phenomena based on scientific theories and models.
7.2 The student can connect concepts in and across domain(s) to generalize or extrapolate in and/or across enduring understandings and/or big ideas.

Answers to Prelab Questions

1. Why does the equation for the velocity of sound in air using an echo include a factor of 2 for the distance?

   Since the sound travels from the origin to the boundary and back, the total distance traveled is double the distance from the origin to the boundary.

2. A hiker stands at the entrance to a canyon and shouts. The echo is heard by the hiker 0.6 seconds later. The temperature of the air in the canyon is 19 °C. How far is the hiker from the canyon wall?
   {13794_PreLabAnswers_Equation_3}
3. Using Figure 1 from the Background section as a guide, complete the charts below for each harmonic of an air column in open and closed tubes, respectively, where L is the length of the air column. The first harmonic has been completed.
   {13794_PreLabAnswers_Table_1}
4. Use Equation 1 from the Background section and the information from the chart above to determine the fundamental mathematical relationship of the natural frequency (f_n) of an open tube and of a closed tube, respectively, to the speed of sound in air (v) and the length of the tube (L).
   {13794_PreLabAnswers_Equation_4}

Sample Data

Introductory Activity

Distance to wall: 45 m
Temperature: 23.5 °C

Analyze the Results

• Calculate the speed of sound in air using the timing of the echoes.
  {13794_Data_Equation_5}
• Determine the theoretical speed of sound by factoring in the affect of temperature.
  {13794_Data_Equation_6}
• Calculate the percent error between the theoretical and experimental values for the speed of sound.
  {13794_Data_Equation_7}
• Identify sources of error that may account for discrepancies between the calculated and theoretical speed of sound.

  The relative humidity of the air may be a factor in how fast the sound waves travel. This is a systematic error that pertains to the conditions of the experiment. One could research a method for measuring and factoring in relative humidity on the speed of sound. Accurate timing with a stopwatch is difficult, and at times the consistency of the cadence of the claps was questionable. The effects that timing errors may have on the experimental results can be mitigated by conducting a large number of trials, employing several timekeepers per trial, and eliminating clear outliers from data sets.

Guided-Inquiry Design and Procedure

Analyze the Results
Calculate the speed of sound in the closed tube. Calculate the theoretical speed of sound for the air in the tube and determine the percent error. Identify sources of error in the experiment.

Temperature of air in tube: 21.7 °C. Since f = 86.073/L and f = v/4L, v = 4(86.073) = 344.3 m/s. The theoretical speed at the measured temperature is: Percent error = 0.03%

Systematic sources of error include the accuracy of each individual tuning fork. Relative humidity was also not factored in for the speed of sound. Random sources of error include the precision of the metric ruler and finding the exact length of the air column where the sound was loudest. The tuning fork needed to be struck repeatedly as the sound diminished over time. The water in the clear tube formed a meniscus, and the bottom of the meniscus changed somewhat depending on exactly how the PVC pipe was held—whether in the center of the clear tube or nearer to one side.

Answers to Questions

Guided-Inquiry Design and Procedure

1. Vibrating tuning forks produce sound waves at known frequencies. Each tuning fork vibrates most strongly at its fundamental frequency (first harmonic), which is stamped on the instrument. If a vibrating tuning fork were used to drive a sound wave in a closed tube, what would be the relationship of the frequency to the length of the air column and the speed of the sound wave when resonance is achieved?

   For a closed tube, the first harmonic occurs at a wavelength equal to 4 times the length of the vibrating column of air, λ = 4L. Substituting the relationship between frequency and wavelength from Equation 1 gives v/f = 4L or f = v/4L.

2. Assume the length of the tube described in Question 2 can be varied. How would you know when resonance is achieved?

   When the tube is the correct length, the sound from the tuning fork will be loudest. At this point, the standing wave of the air column in the tube is resonating with the natural frequency of the tube.

3. Predict how the length of the air column in a closed tube will vary as the frequency of the tuning fork changes.

   The frequency of the tuning fork and the length of the air column are indirectly proportional. As the frequency of the tuning fork increases, the length of the air column will decrease.

4. How might the setup pictured be used to create resonance at different frequencies?

   The water in the tube creates a closed end. The length of the air column is from the open end of the tube to the closed end, or the level of the water. By raising the inner tube, the level of the water changes, thus changing the length of the air column in the tube. If a sound wave were driven into the tube, the tube could be raised or lowered until the sound was loudest, indicating resonance had been achieved. The amount the tube is raised or lowered can be adjusted for different frequencies.

5. Write a step-by-step procedure for measuring the speed of sound in a closed tube using tuning forks. Construct a data table that clearly shows the data that will be collected and the measurements that will be made.
6. How can the data be presented graphically to show a linear relationship between the variables and to calculate the speed of sound?

   Since an inverse relationship exists between frequency and the length of the air column, a graph of frequency versus 1/L should be presented. Since f = v/4L, the speed of sound can be calculated by multiplying the slope of the graph by 4.

Review Questions for AP^® Physics 1 

1. Compare the accuracy of the two methods for determining the speed of sound in air—timing echoes and achieving resonance in a closed tube. How might the accuracy of each method be improved?

   Using tuning forks to achieve resonance in a closed tube was more accurate than timing echoes, 0.03% error compared to 4%, respectively. The greatest source of error for the Introductory Activity was the timing of the claps. The claps are louder than the echoes, and the cadence was rather fast, so it was hard to tell if the cadence was exactly right. Using a digital microphone with a computer program to time an echo would provide more accurate results. The accuracy of the tuning fork method was excellent. It can be noted that calculating the speed of sound for each individual tuning fork resulted in a range of 332.8 – 360.0 m/s, with the greatest percent error of 4.5%, which is still very good. The accuracy of the tuning forks could be verified with an oscilloscope.

2. How would the slope of graphed data for the guided-inquiry activity change if hot water were used instead of room temperature tap water?

   If hot water had been used, then the temperature of the air in the PVC pipe would have been warmer. Therefore, the speed of sound would have been greater than at room temperature, and the slope of the graph would have been steeper.

3. The PVC tube used in the guided-inquiry activity is 61 cm long. Of the eight tuning forks available in this activity, what is the lowest frequency tuning fork that would be able to resonate in the PVC tube at the next higher harmonic? Explain your reasoning.

   The next higher harmonic for a closed tube is f3. Using the maximum length of the closed tube,

   {13794_Answers_Equation_9}

   The lowest frequency tuning fork that could be used to achieve resonance at the third harmonic is 426.7 Hz. Any tuning forks with a lower frequency would require a pipe longer than 61 cm.

4. A boat on Lake Michigan is outfitted with an echo sounder—a type of sonar unit that sends a wave pulse downward and then detects the pulse reflected from the lake bottom. If the time between the incident pulse and the detection of the reflected pulse is 0.27 seconds, how deep is the lake bottom, assuming the speed of sound in the water is 1500 m/s?

   2d = 1500 m/s x 0.27 s
   d = 202.5 m

5. Most orchestras tune to concert pitch, which is 440 Hz.
   1. A clarinet is considered a closed tube, since the musicians’s mouth covers the vibrating reed on the mouthpiece. What is the length of the air column in the clarinet when it is in tune at concert pitch? Assume the temperature of the room is 20 °C.

      f = v/4L
      L = v/4f

      {13794_Answers_Equation_10}

      L = 0.2 m

   2. A flute is an open tube. What is the length of the air column in the flute when it is in tune at concert pitch in the same room?

      f = v/2L
      L = v/2f

      {13794_Answers_Equation_11}

      L = 0.4 m

   3. A piccolo is like a small flute, just 32 cm long. Can the piccolo tune to the fundamental frequency of concert pitch in the same room? If not, how can a piccolo tune with the orchestra?
      {13794_Answers_Equation_12}

      No, the lowest fundamental frequency at which the piccolo can play is 537 Hz. Therefore, the piccolo would have to play at the second harmonic of concert pitch, or 880 Hz (f₂ = 2f₁).

References

AP^® Physics 1: Algebra-Based and Physics 2: Algebra-Based Curriculum Framework; The College Board: New York, NY, 2014.

HyperPhysics. Speed of Sound in Air. http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe.html (accessed June 2014).

Introduction

Lightning flashes and we see it immediately, then a few seconds later we hear a thunderclap. Since light travels faster than sound, counting the seconds between the lightning and thunder gives us an approximation of how far away the lightning flashed. Just how fast does sound travel? How can the speed of sound be measured?

Concepts

• Reflection
• Sound waves
• Resonance
• Frequency and wavelength
• Standing waves
• Speed of sound

Background

Sound is a mechanical wave created by the vibrations of material objects. A mechanical wave requires a medium in order to propagate. Sound propagates by pushing molecules back and forth. If no molecules are present, such as in a vacuum, sound will not travel.

As a sound wave travels through a medium, it may encounter a boundary, or interface of two different media. Upon reaching a boundary, the energy of the sound wave may be reflected, transmitted, or absorbed—often a combination of the three. An echo is an example of a sound wave that is mostly reflected. The difference in time, t, between the creation of the sound wave and the perception of the reflected sound is an indication of the distance to the boundary. If the boundary is a solid, flat object such as a wall, and the distance, d, from the origin of the sound to the boundary is known, the speed of sound can be calculated using the equation, v = 2d/t.

Reflection of sound waves also comes into play in many musical instruments. Woodwind and brass instruments produce sound as air is vibrated in an air column. The length of the air column is varied to change the pitch of the sound produced. The vibrating source produces a sound wave that moves through the air column and is ultimately reflected back toward the vibrational source. The sound produced is the loudest when the air column is in resonance with the vibrational source.

How does resonance occur? The sound wave in the air column consists of alternating high- and low-pressure variations. 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 incident and reflected waves constructively interfere with each other. A standing wave is produced, creating resonance. A standing wave in a column of air can be represented by a sine wave in either an open tube (open at both ends) or a closed tube (closed at one end). A standing wave in an open tube has an antinode at each end, which is the boundary between the air in the enclosed region of the tube and the air outside the tube. In a closed tube, the closed end acts as a fixed point, which prevents movement, and the reflected wave will be inverted. Therefore, the closed end of the tube will always contain a node (see Figure 1). Because the amplitude is largest at an antinode, the sound is the loudest at this point.

Standing wave patterns are only created at an instrument’s natural frequencies, known as harmonic frequencies. The fundamental frequency (f₁) corresponds to the first harmonic. Each harmonic is an integral multiple of the fundamental frequency (f_n = nf₁). As the frequency is increased, additional resonance lengths are found at half-wavelength intervals. An open tube resonates when its length is an even number of quarter wavelengths (e.g., 2, 4, 6), or every half-wavelength. A closed tube resonates when its length is an odd number of quarter wavelengths (e.g., 1, 3, 5).

The speed of sound can be calculated using Equation 1. According to Equation 1, if the frequency (ƒ) and wavelength (λ) of a sound wave are known, the speed of sound (v) can easily be calculated by multiplying the two values together. where

v is the speed (m/s)
ƒ is the frequency (Hz)
λ is the wavelength (m)

The speed of sound is not a constant value and varies depending on the medium in which it travels. At 0 °C the accepted value for the speed of sound in dry air is 331.4 m/s. As the temperature of air increases, the speed of sound also increases because molecules in hot air move more rapidly and collide more often than molecules in cool air. Equation 2 shows the temperature dependence factor for the speed of sound in dry air. where

T is the temperature in degrees Celsius.

Experiment Overview

The purpose of this advanced inquiry lab is to investigate methods for measuring the speed of sound in air. The investigation begins with an introductory cooperative class activity to determine the speed of sound in air using echoes. The experimental wave speed will be compared to the theoretical value. In the guided-inquiry section of the lab, an experiment to measure the speed of sound in a closed-end air column will be designed using tuning forks of known frequencies.

Materials

Prelab Questions

1. Why does the equation for the velocity of sound in air using an echo include a factor of 2 for the distance?
2. A hiker stands at the entrance to a canyon and shouts. The echo is heard by the hiker 0.6 seconds later. The temperature of the air in the canyon is 19 °C. How far is the hiker from the canyon wall?
3. Using Figure 1 from the Background section as a guide, complete the charts below for each harmonic of an air column in open and closed tubes, respectively, where L is the length of the tube. The first harmonic has been completed.
   {13794_PreLab_Table_1}
4. Use Equation 1 from the Background section and the information from the chart above to determine the fundamental mathematical relationship of the natural frequency (f_n) of an open tube and of a closed tube, respectively, to the speed of sound in air (v) and the length of the tube (L).

Safety Precautions

Use caution when clapping the wood blocks together so fingers will not get pinched. Wipe up any water spills immediately. Please follow all laboratory safety guidelines.

Procedure

Introductory Activity (Cooperative Class Activity)

Read the entire Procedure before beginning. Construct an appropriate data table to record measurements and the results of calculations.

1. Locate a spot outdoors at least 20 m away from a large, flat wall with nothing between the spot and the wall that might interfere with sound wave propagation. A greater distance, 50 m or more, is preferable.
2. Record the ambient temperature.
3. One person should stand at the measured spot with the hinged wood blocks and clap them together once. Clap the blocks with the broad side of the blocks facing the wall.
4. Several other people should sit or stand by the “clapper” the same distance away from the wall and listen for the echo.
5. One or more persons stand nearby, each with a stopwatch or timer.
6. The clapper should repeat step 3 until the time between the clap and when the echo is heard is fairly certain. The others listening for the echo can signal when the echo is heard.
7. The clapper now claps the blocks together repeatedly so that each subsequent clap is created at the same time the echo of the previous clap is heard. The listeners can signal when synchronization of the claps and echoes has been achieved.
8. When the claps are in synchronization with the echoes, the clapper counts down in time with the claps, “3, 2, 1, zero,” and immediately counts back up to a set number of claps (10 to 30 claps is usually sufficient for timing).
9. At “zero” the timers start timing and stop when the set number of claps is reached.
10. Repeat steps 7–9 several times to determine precision.

Analyze the Results

• Calculate the speed of sound in air using the timing of the echoes.
• Determine the theoretical speed of sound by factoring in the affect of temperature.
• Calculate the percent error between the theoretical and experimental values for the speed of sound.
• Identify sources of error that may account for discrepancies between the calculated and theoretical speed of sound.

Guided-Inquiry Design and Procedure

Form a working group with other students and discuss the following questions.

1. Vibrating tuning forks produce sound waves at known frequencies. Each tuning fork vibrates most strongly at its fundamental frequency (first harmonic), which is stamped on the instrument. If a vibrating tuning fork were used to drive a sound wave in a closed tube, what would be the relationship of the frequency to the length of the air column and the speed of the sound wave when resonance is achieved?
2. Assume the length of the tube described in Question 2 can be varied. How would you know when resonance is achieved?
3. Predict how the length of the air column in a closed tube will vary as the frequency of the tuning fork changes.
4. How might the setup pictured below be used to create resonance at different frequencies?
   {13794_Procedure_Figure_2}
5. Write a step-by-step procedure for measuring the speed of sound in a closed tube using tuning forks. Construct a data table that clearly shows the data that will be collected and the measurements that will be made.
6. How can the data be presented graphically to show a linear relationship between the variables and to calculate the speed of sound?

Analyze the Results
Calculate the speed of sound in the closed tube. Calculate the theoretical speed of sound for the air in the tube and determine the percent error. Identify sources of error in the experiment.

Student Worksheet PDF

13794_Student1.pdf