Experiment 2
PROPERTIES OF SOUND

PRELAB


VIDEO  Look at a preview of the laboratory activities.

PURPOSE

To observe the waveforms of sound and their characteristics of frequency, period, amplitude and harmonic content. Qualitative properties of the sounds produced by the human voice will be studied.

EQUIPMENT  microphone w/DataLogger interface, tuning fork, call bell, human subjects, copper tube.

RELEVANT EQUATIONS

Frequency-Period
Wave Velocity

DISCUSSION

Sound is a wave phenomenon. As it propagates through air or any other gas, it is a disturbance in the pressure above or below the average ambient value. Together with the pressure disturbance, there are disturbances in the displacement and the speed of the gas molecules. As a wave, sound travels at a constant speed under conditions of fixed temperature and pressure. A snapshot representation of the pressure disturbance produced by a sound wave is illustrated in Figure 2-1. This picture is schematic only, because we can never draw enough dots to represent the huge number of air molecules present at a given point. Also, bear in mind that the pattern propagates (moves) with time. If the sound wave is traveling to the right, then the pattern is continuously moving, and so cannot be easily represented with a still picture.

Figure 2-1: Schematic Representation of Molecular Density
in a Sound Wave

As you can see, at some points the molecules are squeezed more tightly together than normal and the pressure is higher there; these are referred to as compression regions. At other points the molecules are farther apart than normal, and the pressure is lower there; these are referred to as rarefaction regions. Rather than represent the sound wave with a drawing of the molecules, it is more instructive to make a plot of the pressure variation itself, as illustrated in Figure 2-2, where the pressure is plotted against position for three successive times: t1, t2, and t3.

A periodic sound wave is a disturbance that repeats itself in space and in time. If we take a snapshot picture of the pressure pattern of a pure musical sound wave, the natural repetition length is defined to be the wavelength, λ. This type of waveform is referred to as sinusoidal, because the mathematical function that represents this pattern is the sine function.

Likewise, if we focus on a specific location in space and observe the periodic time dependence of the wave disturbance, we can define the repetition time, or period T. A related quantity is the rate of temporal oscillation, or frequency f. The frequency is the reciprocal of the period.

(1)

Since any point on the periodic wave travels a distance of one wavelength in a time of one period, we can relate the wave speed to these two quantities.

(2)

Figure 2-2: Graphical Representation of a Sinusoidal Sound Wave

The latter expression relating the wave speed to the product of frequency and wavelength is perhaps the most widely used.

The intensity of a sound wave, as you would perceive it with your ear, is related to the square of the amplitude of the sound wave. The amplitude is equal to the amount by which the wave pressure deviates above or below the ambient value. When speaking of a pressure wave, the amplitude is measured in units of pressure, N/m2.

An amazing property of periodic waves in general is the fact that any periodic wave of a given frequency, no matter what shape its waveform, can be synthesized by adding sinusoidal waves consisting of the original wave's frequency plus a collection of integral multiples of that frequency. This process is called harmonic synthesis, because the multiples of the base frequency are called its harmonics. The base frequency is called the first harmonic or sometimes, the fundamental. The sinusoidal wave at twice the fundamental frequency is called the second harmonic, etc. By combining a fundamental sound with its harmonics at various amplitudes, a perceptible difference in what we call the timbre of the sound can be detected with the ear. The fact that you can tell a trumpet and a piano apart even though they are playing the same (fundamental) note is due in part to the different harmonic content of the sounds that each instrument produces. In this experiment, you will study the properties of sound waves that are generated by a number of different vibrating objects.


Print out and complete the Prelab questions.