# Sound Wave Interference Tube

## Student Laboratory Kit

### Materials Included In Kit

Funnels, polypropylene, 2
Tubing connectors, Y-shaped, glass, 2
Tubing, latex 2.5 feet
Tuning fork, 512-Hz

Petroleum jelly
Marker
Ruler
Scissors
String (if needed)
Thermometer (may be shared between groups)
Tuning fork activator or rubber mallet
Tuning forks, various frequencies (optional)

### Prelab Preparation

Cut the tubing into two 6-cm pieces and one 11-cm piece, which will leave one leftover long piece, about 53 cm. Note: The long piece will be the piece cut to fit to create destructively interfering waves.

### Safety Precautions

Wear safety glasses and gloves when working with glass tubing. Handle glass tubing with care, and dispose of all broken glass in a broken glass receptacle. Please follow all laboratory safety guidelines.

### Disposal

All materials in this laboratory may be saved and stored for future use

### Lab Hints

• This laboratory activity can reasonably be completed in one 50-minute class period. The prelaboratory assignment may be completed before coming to lab, and the data compilation and calculations may be completed the day after the lab.
• In order to experiment with alternative tuning forks, additional tubing may be required. Latex Tubing, ½" i.d. (Flinn Catalog No. AP2080) makes a good substitute.
• A sound meter, or microphone, can be used to measure and visualize the superposed wave produced by interference. Other tuning forks, or an audio oscillator, may be used to test the tube with other frequencies. This lab may also be done with an oscilloscope and audio frequency generator.

### Teacher Tips

• This activity fits well in any waves and sound curriculum. Use it to introduce the concept of wave interference.
• Students may be curious about the true calculation for the speed of sound in a medium. The equation is as follows:
{12098_Tips_Equation_3}
where

υ is the speed of sound
β is the bulk modulus of the medium
ρ is the density of the medium

Bulk modulus is specific to each type of material, and refers to how much a material will change volume for a given amount of pressure. Temperature, relative humidity, and relative salinity will all affect how a sound wave propagates through air. Compare this to water—although the density of water is generally 1000 greater than air, water is much more incompressible than air, and thus has a much higher bulk modulus—it’s over 100,000 times greater. Consequently, the speed of sound in water at 20 °C is much higher—1482 m/s!
• For further clarification on the topic, you may wish to demonstrate interference for your classroom using wave pulses. Obtain a long string and attach it to a solid object such as a desk. Hold the string out so it hangs horizontally above the floor. Gently send one wave pulse down. Allow it to reflect, and send another wave pulse toward it, both vertical and horizontal. With practice, both constructive and destructive interference may be demonstrated. If the crests are on the same side, the two pulses should combine briefly to form a super wave, and re-separate afterwards. If one is a crest and the other is a trough, the waves should momentarily disappear, only to reappear on either side of their connection point.
• Look into the Flinn Scientific Waves and Sound—Student Laboratory Kit, Catalog No. AP7014, for a comprehensive set of experiments involving waves and sound.

### Science & Engineering Practices

Developing and using models
Planning and carrying out investigations
Using mathematics and computational thinking

### Disciplinary Core Ideas

MS-PS4.A: Wave Properties
HS-PS4.A: Wave Properties

### Crosscutting Concepts

Patterns
Cause and effect
Systems and system models

### Performance Expectations

MS-LS2-2: Construct an explanation that predicts patterns of interactions among organisms across multiple ecosystems.
MS-LS2-4: Construct an argument supported by empirical evidence that changes to physical or biological components of an ecosystem affect populations.
HS-LS2-2: Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales.

1. Two waves are interfering constructively. If one of the waves is removed, the sound volume will:

increase / remain unchanged / decrease.

2. Two waves are interfering destructively. If one of the waves is removed, the sound volume will:

increase / remain unchanged / decrease.

3. If the temperature of a room is 22.3 °C, what is the speed of sound?

Using Equation 1, 331.4 + 0.6T = 331.4 + 0.6*(22.3) = 344.8 m/s

4. With the above room temperature, what is the wavelength of a 256-Hz sound wave?

Using Equation 2, ν = λf, 344.8 m/s = λ* 256 s–1, λ = 1.35 m

5. Answer Questions 3 and 4 for a hotter temperature of 38.0 °C.

Using Equation 1, 331.4 + 0.6T = 331.4 + 0.6*(38.0) = 354.2 m /s. Using equation 2, ν = λf, 354.2 m/s = λ* 256s–1, λ = 1.38 m

### Sample Data

Room temperature: ___23 °C___
Speed of sound at room temperature: ___345.2 m/s___
Tuning fork frequency: ___512 Hz___
Tuning fork wavelength: ___0.67 m___
Half-wavelength: ___0.34 m___
Total path length (for destructive interference): ___45 cm___

Observations

{12098_Data_Table_1}

1. What happens when the pinched tube is released? Explain.

When the pinched tube is released, the sound is allowed to travel through both tube lengths. Because one tube length is half a wavelength longer than the other, the peak amplitude of one sound wave meets the trough amplitude of the other, which cancels out and results in no (or very little) sound when the waves recombine.

2. Why is it important to take air temperature into account when calculating path length?

On a hotter day, sound travels faster, which means the wavelength of the sound will be longer. When the wave splits, one path length will need to be a little longer on a hot day to account for this difference.

3. How would the set-up used in this activity have to be modified in order to demonstrate destructive interference using a 384-Hz tuning fork?

The same set-up would not be appropriate, as the half-wavelength for 512 Hz would be different than for 384 Hz, thus there would be no destructive interference. However, the same principle applies, and by calculating the half-wavelength for 384 Hz and adjusting the path lengths as necessary, destructive interference could be created.

4. Speculate on how a noise canceling device might work.

A noise canceling device might work by taking any incoming sound wave, and generating an identical wave offset by ½ of the wavelength. That way, total destructive interference would occur, and the noise would be reduced or even eliminated.

### References

Halliday, D., Resnick, R., & Walker, J., Fundamentals of Physics, 8th ed.; Wiley: Cleveland, OH, 2008.

Hyperphysics: Georgia State University, http://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.html, (accessed May 2010).

# Sound Wave Interference Tube

### Introduction

Send a sound wave along two paths of different lengths. What happens if one path is blocked? The result may be surprising. When sound waves interfere with each other, two outcomes are possible. They may reinforce each other and sound much louder. Alternatively, they may also interfere destructively, sounding much quieter or, in some cases, having no sound at all. Demonstrate this effect using a Quincke’s interference tube.

### Concepts

• Interference
• Sound Waves
• Principle of superposition
• Constructive vs. destructive interference

### Background

Sound is a mechanical wave created by the vibrations of material objects. A mechanical wave requires a medium in order to propagate. In other words, for sound to travel, some type of substance must be present (solid, liquid or gas). A substance is needed because sound propagates by pushing molecules back and forth. If there are no molecules to move, such as in a vacuum, sound will not travel.

Like any waves, sound waves can combine with each other. The process of two waves combining is called interference. According to the principle of superposition, when two waves interfere, the resultant wave is simply the sum of the two. The term interference does not imply the overlapping waves in any way alter the travel of one another, but refers only to the resulting displacement. Two waves may temporarily interfere, and continue along their paths unchanged. When the crests and troughs line up from two waves of the same frequency traveling in the same direction, they are said to be in phase. When this happens, the waves are reinforced and experience constructive interference. This is shown in Figure 1.

{12098_Background_Figure_1_Constructive interference}
If two waves of the same frequency traveling in the same direction combine so that the crests of one wave line up with the troughs of another, the waves are out of phase, and experience destructive interference. If the amplitude of the two waves is the same, then the sound will cancel out entirely. This is shown in Figure 2.
{12098_Background_Figure_2_Destructive interference}
The speed of sound waves traveling in air depends on a number of factors but, for simplicity’s sake, a calculation can be done in which only the temperature of the air is taken into account. The simple equation for calculating the speed of sound in air is as follows:
{12098_Background_Equation_1}
where

Tc is the temperature of the air (in degrees Celsius)
νsound is the speed of sound (in meters per second)

Note that the units do not in fact work out in this equation. That is because this equation is a simplified version of a more complex understanding of the nature of the speed of sound in a given medium.

The relationship between wavelength, frequency, and speed for any wave is found by Equation 2
{12098_Background_Equation_2}
where

ν is the wave speed
λ is the wavelength
f is the frequency

(Note: It is fairly common for physics textbooks to use the Greek letter nu, ν, rather than f to represent frequency).

### Experiment Overview

The purpose of this activity is to demonstrate destructive interference. By directing the sound wave from a tuning fork down two paths of differing length, the waves will be out of phase. When the path length differs by one half of the wavelength, the waves will experience destructive interference.

### Materials

Petroleum jelly
Funnels, polypropylene, 2
Marker (optional)
Ruler
Scissors
Thermometer
Tubing connectors, Y-shaped, glass, 2
Tubing, latex, 6 cm, 2
Tubing, latex, 11 cm
Tubing, latex, 53 cm
Tuning fork, 512-Hz
Tuning forks, various frequencies (optional)
Tuning fork activator or rubber mallet

### Prelab Questions

Circle the best choice for Questions 1 and 2.

1. Two waves are interfering constructively. If one of the waves is removed, the sound volume will:

increase / remain unchanged / decrease.

2. Two waves are interfering destructively. If one of the waves is removed, the sound volume will:

increase / remain unchanged / decrease.

3. If the temperature of a room is 22.3 °C, what is the speed of sound?
4. With the above room temperature, what is the wavelength of a 256-Hz sound wave?
5. Answer questions 3 and 4 for a hotter temperature of 38.0 °C.

### Safety Precautions

Although latex is not considered hazardous, not all health aspects of this substance have been thoroughly investigated. Latex may be an allergen. Wear safety glasses and gloves when working with glass tubing. Please follow all laboratory safety guidelines.

### Procedure

1. Check the room temperature with the thermometer, and record this value on the Sound Wave Interference Tube Worksheet
2. Using Equation 1 from the Background section, calculate the speed of sound in air and record this value on the worksheet.
3. Obtain a tuning fork and record its frequency on the worksheet.
4. Using the calculated speed of sound and the frequency of the tuning fork, calculate the wavelength of a sound wave produced by the tuning fork and record this value on the worksheet.
5. Divide the value from step 4 by two to find the path length difference for destructive interference, and record it on the worksheet. Hint: Pay attention to units!
6. Take the two 6-cm lengths of rubber tubing and attach each to a base of a polypropylene funnel.
7. Lubricate the outside of the base of each Y-connector with a small amount of petroleum jelly, taking care that no petroleum jelly gets inside the connector.
8. Carefully attach the free end of each tubing piece to the base of each Y-connector (see Figure 3).
{12098_Procedure_Figure_3}
9. Repeat step 7 with the arms of each Y-connector.
10. Take the medium length 11-cm rubber tubing, and carefully fit each end onto one arm of two separate Y-shaped connectors (see Figure 3).
11. Add the length calculated in step 5 to 11 cm for the “longer path length” necessary for destructive interference. Record this value on the worksheet.
12. Measure and cut to length the second longer rubber tube.
13. Carefully slide each end of the long rubber tube over the free arm of a Y-connector. Note: Try to ensure that the amount of overlap between the latex tubing and the glass tubing is approximately equal at all four attachment points.
14. Have one partner hold the assembly carefully, with one funnel held up against the ear. The other partner will activate the tuning fork.
15. When ready, have one partner hold the tuning fork by the base and strike it against the tuning fork activator. After striking the fork, wait a moment for the high-pitch buzz to fade, then hold the tines of the tuning fork near the other free polypropylene funnel.
16. Tightly pinch and release the longer of the two pieces of tubing several times while the other partner notes any audible changes. Record all observations on the student worksheet. Note: If no sound is heard when one tube is pinched, then repeat step 15.
17. Switch partners and repeat steps 14–16.
18. (Optional) Repeat steps 3–17 with other tuning forks provided by the teacher.

### Student Worksheet PDF

12098_Student1.pdf

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