Experiment 12: Speed of Soundin Air

Experiment 12: Speed of Sound in Air

Figure 12.1: Sound Tube

EQUIPMENT

Sound Tube

(3) Tuning Forks (f ¡Ý 300 Hz)

Mallet

Water Jug

Rubber Hose

Clamps and Rod

Paper Towels

Figure 12.2: Displacement of Air

61

Experiment 12: Speed of Sound in Air

62

Advance Reading

Text: Speed of sound, longitudinal waves, wavelength,

frequency, standing wave, resonance.

Objective

The objective of this experiment is to measure the

speed of sound in air.

When considering the displacement of air for resonance

(constructive interference), notice that there is an antinode near the open end of the tube, and a node at the

water¡¯s surface from which the sound is reflected (refer to Fig. 12.2). To locate multiple resonances for a

particular tuning fork, one must be able to change the

length of the air column in the tube. This will be accomplished by adjusting the water level in the tube:

raise or lower the water reservoir, and the water level

in the tube will change accordingly.

Theory

There are a variety of wave types.

Sound is a longitudinal wave requiring a medium in

which to propagate. A longitudinal wave is one in

which objects oscillate in the same direction the wave

propagates. The speed of sound depends on properties of the medium such as bulk modulus, density, and

temperature. The speed of sound is not a constant

value!

To calculate today¡¯s speed of sound, v, we will determine the wavelength, ¦Ë (lambda), of the sound produced by a tuning fork of known frequency, f :

v = ¦Ëf

(12.1)

A vibrating tuning fork generates a sound wave that

travels outward in all directions. When held above a

sound tube, a portion of the wave will travel down the

tube, reflect off the water¡¯s surface, then return to the

top. If the rising pressure wave reaches the top of the

tube as the next wave is produced, the wave is reinforced, and the sound will resonate. A standing wave is

generated in the tube, and the sound will be distinctly

louder. This occurs when the column of air in the tube

has an appropriate length (height) for a given tuning

fork.

The distance between one resonance and the next is

1

2 ¦Ë. This experiment will attempt to locate at least

three resonances to reduce uncertainty of the results.

¦Ë

= |x1 ? x2 |

2

(12.2)

Having calculated ¦Ë and being given f of a tuning fork,

the speed of sound can be calculated with Eq. 12.1.

Prelab 12: Speed of Sound in Air

63

Name:

1. What is a standing wave? (20 pts)

2. What is a resonant frequency? (20 pts)

3. Explain the relationship v = ¦Ëf . (20 pts)

4. Refer to Eq. 12.1 and Eq. 12.3 (Step 10 of the procedure). You measure 12 ¦Ë to be 40 cm. The temperature in the

lab is 22? C. What is the frequency of this resonance? (40 pts)

Experiment 12: Speed of Sound in Air

64

PROCEDURE

QUESTIONS

1. Raise the bottle of water until the tube is filled.

2. Hold a vibrating tuning fork above the tube and

lower the water level gradually until the sound becomes loudest (resonates). Raise the water level as

necessary.

3. Mark the water level with a rubber band.

4. Continue to lower the water level until all resonant

positions have been marked in this manner. Record

the positions in the data table provided.

1. Define ultrasonic, supersonic, and infrasonic.

2. As noted in the theory section, our sound tubes do

not have an anti-node at the open end of the tube.

Analyze your data and determine where, relative to

the open end of the tube, the anti-node is located

for each frequency used. State your answer in terms

of ¦Ë. Refer to Fig. 12.

5. Calculate the average distance ¡°l¡± between resonance positions. Record it in the table provided.

3. Assume you are in a particular location (e.g., at the

beach, in the mountains, in the lab). Two sounds,

one a high frequency, one a low frequency, are generated. Does a high frequency sound travel faster

than a low frequency sound in a particular location?

6. Calculate the fundamental wavelength ¦Ë = 2l and

record it.

4. Does sound travel at the same speed in different

materials? Specify the speed of sound in 3 media.

7. Calculate the measured speed of sound ve = f ¦Ë and

record it.

8. Repeat this process for two other frequencies (3 tuning forks, total).

9. Average your three values of v. Record them in the

data table on the board.

10. Calculate a theoretical value for the speed of sound,

vT , using:

vT = (331.5 + 0.6T )m/s

= d1 + d2

1

4¦Ë

= distance from position of water¡¯s surface

when 1st resonance is heard to anti-node.

(12.3)

where T is the temperature in degrees Celsius.

11. Calculate your percent error. [Eq. A.1, Page 141]

Figure 12.3: Proper position for tuning fork

1

4¦Ë

d1 : Refer to Step 2.

d2 ¡Ô distance from the top of the tube to the

anti-node.

Figure 12.4: Determination of anti-node location.

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