Production and Characteristics of Sound

1A drumbeat across the valley

When intore dancers perform, the ingoma drums can be heard far across a valley. The drummer's stick hits a stretched cowhide; the hide moves in and out hundreds of times a second, and a listener on the next hill hears the beat a moment later. Nothing solid travels between the drum and the ear. What travels is a disturbance in the air: a sound wave. In S5 you studied progressive and stationary waves on strings. This unit applies those ideas to sound, the waves your national examination asks about most.

2Experiment 1.1: does sound need a medium?

Apparatus: an electric bell hung by its wires from a rubber bung, a glass bell jar on a greased base plate, a vacuum pump, a battery and a switch (Figure 1.1).

Figure 1.1: The bell-jar experiment. The wires pass through the bung, so the bell can be switched on from outside while the air is pumped out.

1. Switch the bell on. You hear it clearly and see the hammer striking the gong.
2. Start the pump. As the air is removed the sound grows fainter, although you can still SEE the hammer striking.
3. Let the air back in slowly. The sound returns.

Conclusion: a vibrating source needs a material medium (solid, liquid or gas) to carry its sound. Light crosses the vacuum, which is why you still see the hammer. A faint sound usually remains even at the lowest pressure, because some vibration passes through the bung, the wires and the air the pump cannot remove.

3How a vibrating source makes a longitudinal wave

Think of a loudspeaker cone. As it moves forward it pushes the layer of air in front of it, squeezing that layer against the next one: a region of higher pressure, a compression, moves off. As the cone moves back, the air in front of it spreads out into a region of lower pressure, a rarefaction. Each layer of air only oscillates back and forth about its own position, along the direction in which the wave travels, so sound is a longitudinal wave.

Figure 1.2: A sound wave frozen at one instant. Top: the air layers (C = compression, R = rarefaction). Middle: the excess pressure $\mathrm{\Delta }p\backslash Delta\; p$. Bottom: the displacement $ss$ of each layer, positive in the direction of travel.

Look carefully at the two graphs. At the centre of a compression the layers on the left have moved forward (positive $ss$) and the layers on the right have moved back, so the layer in the middle has not moved at all: the displacement is zero where the pressure change is greatest. The pressure wave and the displacement wave are a quarter of a wavelength ($\frac{\pi }{2}\backslash frac\{\backslash pi\}\{2\}$ rad) out of step. You will use this again for pipes in lesson 3, where a displacement node is a pressure antinode.

4Displacement and pressure amplitudes

For a sound wave travelling in the $+x+x$ direction the displacement and the excess pressure are

where $k=\frac{2\pi }{\lambda }k\; =\; \backslash frac\{2\backslash pi\}\{\backslash lambda\}$ and $\omega =2\pi f\backslash omega\; =\; 2\backslash pi\; f$. The pressure change is caused by the squeezing of the layers, $\mathrm{\Delta }p=-B\frac{\mathrm{\partial }s}{\mathrm{\partial }x}\backslash Delta\; p\; =\; -B\backslash ,\backslash frac\{\backslash partial\; s\}\{\backslash partial\; x\}$, where $BB$ is the bulk modulus of the medium. Differentiating $ss$ gives $\mathrm{\Delta }p=Bk{s}_m\sin (kx-\omega t)\backslash Delta\; p\; =\; B\; k\; s\_m\; \backslash sin(kx\; -\; \backslash omega\; t)$, so $\mathrm{\Delta }{p}_m=Bk{s}_m\backslash Delta\; p\_m\; =\; B\; k\; s\_m$. Using $v=\sqrt{\frac{B}{\rho }}v\; =\; \backslash sqrt\{\backslash frac\{B\}\{\backslash rho\}\}$ (lesson 2), $B=\rho v^{2}B\; =\; \backslash rho\; v^2$, and $k=\frac{\omega }{v}k\; =\; \backslash frac\{\backslash omega\}\{v\}$:

5The characteristics of a sound

Three words describe how a sound seems to a listener. Each is linked to a physical property of the wave.

A microphone connected to an oscilloscope (CRO) turns each sound into a trace of voltage against time, so the three characteristics can be seen. In Figure 1.3 every screen uses the same settings.

Figure 1.3: Oscilloscope traces of four notes, each screen 8 divisions wide and 4 divisions high.

6The limits of audibility

A young person with healthy ears hears frequencies from about 20 Hz to 20 000 Hz. Sound below 20 Hz is infrasound; earthquakes and large machines produce it, and it can sometimes be felt as a vibration. Sound above 20 kHz is ultrasound. Other animals hear different ranges: dogs up to about 30 kHz, and bats and dolphins up to about 100 kHz. With age the upper limit falls, a loss called presbycusis, so many adults cannot hear a 15 kHz tone that a teenager hears clearly.