Experiment 12

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

Sound is a wave phenomenon. As it propagates in air or any other gas, it changes the pressure above or below the average ambient value. In conjunction with the pressure changes, there are also changes 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 12-1. 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 sound wave is traveling, so the pattern is continuously moving and thus cannot be easily represented with a still picture.

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 12-2, 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 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 variation of the displacement, we can define the repetition time, or period T. A related quantity is the frequency f. The frequency is the reciprocal of the period:

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.

This last expression, v = f λ, relating the wave speed to the product of frequency and wavelength, is perhaps the most widely used.

The intensity of a sound wave, the loudness as you would hear it, is related to 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 integer 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 heard. 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.