Experiment 3
THE VELOCITY OF SOUND IN AIR

PRELAB


VIDEO  Look at a preview of the laboratory activities.

PURPOSE

To study the longitudinal (compressional) wave motion of sound by determining the velocity of sound in air using a resonance tube and using the measured velocity to calculate the frequency of a mystery sound.

EQUIPMENT   Kundt's tube standing wave apparatus, audio oscillator, microphone or hearing tube, meter stick, thermometer.

RELEVANT EQUATIONS

Speed of Sound vs = f λ
Distance between Adjacent Nodes d = λ / 2

DISCUSSION

Sound in a gas like air is a longitudinal disturbance in the pressure and displacement of the molecules. It is clear from a simple experiment that sound travels at a relatively fast but finite speed. There is no perceptible delay in the sound that arrives at your ears when a person located across the room is speaking. However, if a lightning flash occurs 5 miles away, it takes a significant amount of time before the accompanying thunderclap arrives at your ear.

In this experiment, you will examine the relationship between the wave speed, frequency and wavelength of sound, and in the process, make a determination of the speed of sound. The technique to be used is the method of standing waves. Standing waves are produced when two waves of nearly equal amplitude propagate in opposite directions along the same medium. A pattern of loops, or Antinodes is produced, each of which spans one-half wavelength. By measuring the distance between the quiet points, or Nodes in the pattern, a determination of the wavelength of the sound can be made. If the frequency of the sound is known or measured by other means, then the speed of the sound waves can be determined through the basic wave relation:

vs = f λ (1)


Figure 3-1: Resonance Tube Apparatus

Consider the resonance tube of Fig. 3-1. Assume the piston is in position B. Sound energy of a definite frequency enters the tube at A from a small speaker. A small amount of energy entering at A will go through the opening at B and to the ear. Most of the sound energy will be reflected at B back to A as in a closed pipe. For specific lengths of the closed pipe, a standing wave is produced, and resonance will occur. The sound heard by the ear will be much louder than it would be if the resonant condition did not exist. As shown in Fig. 3-2, standing waves will be produced under the condition that the positions at B, C, D, etc., are nodes of displacement.


Figure 3-2: Standing Waves and Corresponding Wavelengths in a Closed Tube

Note that the distances between successive points of resonance are each one-half wavelength and so wavelength is twice the distance between resonant points. Thus, if L is the distance between the first and fifth resonant points, the wavelength would be λ = 2 (L / 4), since four loops, or half-wavelength are included. The distance between adjacent nodes d, is equal to one-half of a wavelength:

The source of sound for the resonance tube shown in Fig. 3-1 is a small speaker which is driven by an electronic audio oscillator in which the frequency can be closely controlled. A meter stick along the resonance tube facilitates recording the positions of successive loud points.


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