1

Experiment VWS-4S

VELOCITY OF SOUND IN AIR

Purpose

The purpose of this experiment is to measure the velocity of sound in air by the resonance-tube method.

Community College of Philadelphia

Physics Department

Student Name:______

Partners:______

______

______

Physics Course #:______Section #:______

Date performed:______Date due:______

VELOCITY OF SOUND IN AIR

Purpose

The purpose of this experiment is to measure the velocity of sound in air by the resonance-tube method.

Theory

Wave motion is hardly an unusual phenomenon. Sound waves, light waves, and radio waves, to name just a few, have considerable effects upon our daily lives. Although at first glance the many types of waves which we experience may seem to have very little in common, further study reveals that in certain respects one sort of wave motion is much like any other.

Any type of wave motion is capable of transmitting energy from one location to another by creating a disturbance which propagates through a medium. Interestingly, the medium need not always be a physical medium. Light waves, for instance, will propagate through a vacuum. If a physical medium is involved, however, individual particles of the medium will oscillate up and down or back and forth but will not progress with the wave. Although energy is transferred, the particles themselves remain close to their original positions.

Waves are conveniently classified by the way in which the motion of the individual particles of the medium is related to the movement of the wave itself. A wave in which the vibrating particles move at right angles to the direction in which the wave travels is known as a transverse wave. A wave in which the individual particles vibrate along the direction of propagation is known as a longitudinal wave.

Consider the sound wave generated in air by the tuning fork of Figure 1. The vibrating prongs of the fork strike nearby air molecules and set them in vibration. These air molecules collide with other air molecules farther from the tuning fork and cause them to vibrate also. Soon, groups of air molecules within a considerable distance of the tuning fork are vibrating back and forth with the same frequency as the vibrating prongs of the tuning fork. (The vibrations of the air molecules are, of course, superimposed on the normal random thermal motion of the molecules.) As a result of the molecular vibration, there are certain regions where the air molecules are closer together than normal and where the pressure is slightly higher than the normal atmospheric pressure. These regions are known as regions of compression and are marked with C's in Figure 1. There are other regions where the air molecules are farther apart than normal and where the air pressure is slightly less than the normal atmospheric pressure.

These regions are known as regions of rarefaction and are marked by R's in Figure 1. As the tuning fork vibrates, these regions of compression and rarefaction move outward from the fork in various directions, including that toward the ear of the listener. As the compressions and rarefactions pass the ear, the eardrum vibrates and the listener hears the sound of the tuning fork. Since the air molecules vibrate in the same direction as the wave is moving, a sound wave in air is an example of a longitudinal wave.

The velocity of propagation of the compressions (and rarefactions) in Figure1 is the speed of sound v. The speed of sound in air is approximately v0 = 331.3 m/s at 0 oC. At higher temperatures the speed of sound vt is somewhat higher and is given by equation (1), in which tc is the temperature in oC.

(1)

The number of compressions per second passing a point in space (such as the ear) is known as the frequency f of the wave. This frequency is the same as the frequency of vibration of the source, providing that there is no relative motion between the source and the ear of the listener. The units of frequency are given the name hertz (abbreviated Hz). The distance from the middle of one compression to the middle of the next is called the wavelength. The wavelength is represented by the Greek letter lambda () and may be expressed in units of meters. The velocity, frequency, and wavelength are related by equation (2).

v = f (2)

In this experiment we will assume f to be the frequency of the tuning fork as specified by its manufacturer; we will measure  by the resonance-tube method; and we will determine our measured value of v by substituting these quantities in equation (2).

Figure 2 is a diagram of the resonance-tube apparatus to be used in this experiment. A hollow plastic tube, a centimeter scale, and a water reservoir are supported from a vertical rod. The lower end of the plastic tube is connected to the water reservoir by a piece of rubber hose. The water level in the plastic tube can be varied by raising or lowering the water reservoir. In this way changes can be made in the length of the air column in the plastic tube above the water. It is possible that you may be given a slightly different apparatus on which the centimeter marks are placed directly on the plastic tube instead of on a separate meter stick. There may also be a difference in the clamp that holds the water reservoir on the rod.

Suppose that a vibrating tuning fork is held above the tube as in Figure 3. A sound wave travels down through the air column in the top of the tube and is reflected back upward from the water. The wave is partially reflected again at the open top end of the tube. These waves traveling upward and downward in the tube combine to form a "standing wave". In the standing wave there are certain fixed regions called nodes where there is very little vibration of the air molecules. In the standing wave there are other fixed regions called antinodes where there is a large vibration of the air molecules. Each antinode is separated from the nearest node by a distance of /4, where  is the wavelength of the original traveling wave.

There are certain lengths of the air column (in relation to ) for which the vibrations of the air molecules at the antinodes are especially large. This condition of the air columns is known as resonance. At resonance the energy is removed more rapidly from the tuning fork and the sound becomes louder. Figures 3 a, b, and c show the three resonance conditions possible with your apparatus. The nodes of displacement are marked as "N" and the antinodes are marked as "A". Note that in each resonant case there is a node at the bottom of the air column and an antinode at the open end of the tube. Your apparatus can be adjusted for the three resonant conditions by listening for increases in the loudness of the sound of the tuning fork. The wavelength can be calculated from the length of the air column at resonance. Finally, the speed of sound in air can be calculated using equation (2).

Apparatus

Resonance-tube apparatus

Tuning fork (512 Hz)

Tuning-fork activator

Beaker (1000 ml)

Stethoscope

Centimeter scale

Procedure, Data, and Calculations

Cautionary Notes:a. Water is sometimes spilled accidentally during this experiment. It is

advisable to keep books and other personal property of the table where you

are using the resonance-tube apparatus.

b. A stethoscope is provided if you have difficulty hearing the sound from your

own resonance tube. Its earpieces have been sterilized with alcohol. No

more than one lab partner should use the stethoscope because of the danger

of spreading an ear infection.

1.Measure and record the room temperature to the nearest tenth of a degree Celsius. Read the frequency engraved on the tuning fork and record it on the data table. Measure the inside diameter of the plastic resonance tube with a centimeter scale and record these values below and on the data table.

Room temperature:tr = ______C

Frequency of tuning fork:f = ______Hz

Inside diameter of tube:D = ______cm

2.Set the reservoir cup of the apparatus as high as it will go on the metal rod (i.e., until it bumps into the bracket supporting the top of the plastic tube). Be sure that the rubber tubing is tightly attached at one end to the reservoir and at the other end to the bottom of the plastic tube. Verify that the water level is approximately 14 cm below the top of the tube. If the level is too low, pour water from a beaker into the reservoir to correct this.

3.Strike the tuning fork on the rubber activator. Hold the tuning fork over the plastic tube with one prong directly over the other prong.

4.Slowly lower the water level in the plastic tube by lowering the water reservoir. Adjust the water level until the sound of the tuning fork is reinforced by resonance in the column of air above the water. It may be necessary to reactivate the tuning fork several times while searching for the water level at which the sound of the tuning fork is loudest. You will need to read the water level while it is changing at the instant the sound is loudest. Read the scale next to the plastic tube at this water level to the nearest .02 cm. Record this reading as the resonant length l.

Length of resonant column

of air (reading 1):l = ______cm

5.Correct this value of the length of the air column by adding four-tenths of the diameter of the plastic tube. This correction is necessary because the antinode is not formed at the tube opening, but a little outside of it.

lcorr = l + .4 D

= (Substitute)

= ______cm (Final answer)

6.Since the first resonance occurs at lcorr = /4, the wavelength can be calculated by rearranging this formula.

 = 4 lcorr = (Substitute)

= ______cm (Final answer)

7.Transfer the measured and calculated data from steps 4, 5, and 6 to the data table for reading 1.

8.Strike the tuning fork on the activator again and hold it above the resonance tube. Lower the water level until a second resonant condition is reached. Record this level on the data table as l for reading2. Lower the water level further until a third resonant condition is reached. Record this level on the data table as l for reading 3.

9.Correct these two additional values of l in the same way you did in step 5. Then calculate the wavelengths. For reading 2:  = 4 lcorr /3. For reading 3:  = 4 lcorr /5. Make these calculations on scratch paper and record you results on the data table.

10.Calculate the average wavelength below. Then, convert this wavelength to meters by moving the decimal point two places to the left.

average  = = (Substitute)

= ______cm = ______m (Final answer)

11.Calculate the velocity of sound from your measurements. Use the average value of  from step 10.

vmeas = f  = (Substitute)

= ______m/s (Final answer)

12.Find the accepted speed of sound at your room temperature.

= (Substitute)

= ______m/s(Final answer)

13.Calculate the percent error in your measured value of the speed of sound.

% Error =

= (Substitute)

= ______%(Final answer)

14.Transfer the results of your calculations in steps 10 through 13 to the data table.

Experiment VWS-4Data Sheet

Room temperature:tr = ______oC

Tuning-fork frequency:f = ______Hz

Inside diameter of plastic tube:D = ______cm

Determination of wavelength 

Average = ______cm = ______m

Measured velocity at room temperature:v = f  = ______m/s (Step 10)

Accepted velocity at 0 oC: vo = ______m/s (Step 11)

Accepted velocity at room temperature: = ______m/s

Percent error in measured velocity of sound: ______%

Questions

1.Was your value of the velocity of sound approximately equal to the accepted value, within a reasonably small percent error? What specific defects in the equipment or procedure might have contributed to your error?

2.If the temperature of the room had been lower, would the length of the resonating air column been affected? Explain.

3.Why do you see a flash of lightning before you hear the corresponding clap of thunder (instead of at the same time)?

4.Mention some musical instruments that use hollow tubes or hollow cavities to obtain a resonant condition of the air in the tube or cavity.