## Experiment III-9

Waves: Speed of Sound

Waves pervade the universe.  We experience sound waves and light waves.  Wave mechanics explains atoms and subatomic matter.  Loops of waves of energy called strings have been proposed as the essence of everything in the universe.

Waves in deformable (elastic) matter are called mechanical waves.  Unlike the transverse motions of objects studied earlier, only the disturbance of the wave moves from one location to another while the displaced matter oscillates around to its equilibrium location.  Material can be disturbed by a wave in three distinct directions:

For example in sound, the material can be alternately compressed and rarified in a disturbance that expands outwards from the source.   The wave travels the same direction as the disturbance.   This is called a longitudinal or compression wave.

On the surface of a liquid (e.g., the ocean) or sheet (e.g., a flag) the material is displaced perpendicular to the surface.   For example the surface of the ocean goes up and down as the wave crosses the surface.   This is called a transverse wave.

Cohesive materials may be twisted around the axis of the wave travel (e.g., a lawn hose or a wire) with neighboring parts of the material receiving the twist a very short time later.  This is called a torsional wave.

View animations of severals waves on Dan Russell's web site at Kettering University.  (If using a slow modem, be sure to wait until all three animations load.)

Unlike our common observation that two objects can't occupy the same space, multiple waves can simultaneously occupy the same space.  View the top animation on passing waves on Dan Russel's web site.

### Experiment

It is convenient to label several aspects of a wave:  the distance from one part of a wave, (say its highest value called its crest) to the next similar part of the wave is called the wavelength, commonly labeled with the symbol λ.  The time between the passage of a part of the wave (say a crest) and the next similar part is called the period, T.  The number of waves that pass a location in a unit of time is called the wave's frequency (waves/second = Hertz), commonly labeled with the symbol ν.  Waves carrying more energy are larger in amplitude.

The product of a wave's frequency, ν, and wavelength, λ, gives the speed at which the wave moves, c:
ν   •   λ   =   c
Note that the product of the units of frequency, 1/sec, times that of wavelength, m, produces the units of speed, m/sec.

If a wave strikes a barrier they will reflect.  When a continuous series of waves of uniform frequency are reflected from a barrier, the reflected waves will encounter the incoming waves.  Wherever a reflected crest meets a similar incoming crest, the two waves will momentarily sum creating a double amplitude wave.  Wherever a crest encounters a trough, its opposite, the two waves will cancel creating momentarily a location of near zero amplitude.  This process called interference creates a region of standing waves twice the amplitude of the original wave.  If the waves are sound waves, the regions of constructive interference will be twice as loud while the canceling regions will be nearly silent.  This constructive interference occurs every HALF wavelength.  You may wish to view an animation of such standing waves on the Physics Classroom web site and confirm this.

If a continuous sound enters a tube closed on one end, it will reflect at the closed end causing interference.  But if the open end is relatively small, a significant amount of reflection will occur there as well.  This reflection at the open end can be reduced by flaring the opening as common in many musical instruments.  If the tube is just the right length, reflections from both the closed and open ends will result in a resonance of repeated constructive interference with noticeable amplification.  But if the tube is any other length, the interference will be destructive.  If the sound is a broad buzzing at the closed end created by vibrating lips, only the frequency that is resonant with the length of the tube length will be amplified and produced by the instrument.

In this experiment a single frequency of sound will be produced and the length of the tube modified until it matches that needed to produce resonance and the sound amplified.  Gradually changing the tube length will eventually reach another length which amplifies the sound.  Doubling the product of the frequency of the sound with the difference in length (which is also the minimum length needed for resonance) will calculate the speed of the sound.

### Materials

• computer with speaker to play sound files
• ~60 cm (2 foot) length of straight 1.25" (3.2 cm) diameter PVC pipe (or similar substitute)
• container with ~0.5 m depth water

### Procedure

1. Holding the pipe vertically above the water, play one of the sound files nearby.  Loop the short file in your computer's sound player so that it plays as long as needed.
2. With your ear nearby, slowly lower the pipe into the water until maximum amplification by resonance is found.  When constructive interference of reflected sound waves occurs, one gets the impression that the sound is emitted directly from inside the pipe.  This sensation is caused by the increase in loudness due to this resonance.  The resonance point can be obtained by fine adjustments up and down seeking maximum sound amplitude.
3. Measure the distance between water level and the end of the pipe open to the air, L.
4. Continue lowering the pipe into the water until the next resonance maximum is found and measured.
5. Use the difference in the two distances, ΔL, to calculate the speed of the sound waves, c = 2ΔL • ν.
6. The procedure can be repeated to locate a third resonance point.  Take the average speed.
7. Repeat the process with different frequencies of sound to determine how the speed of sound varies with frequency.

Communicating technical information such as observations and findings is a skill used by scientists but useful for most others.  If you need course credit, use your observations in your journal to construct a formal report.

### References

created 22 March 2005
revised 16 January 2007
by D Trapp