Istituto “Enrico Fermi” Mantova School Year 2011-2012 Physics course The physics of sound.

Istituto “Enrico Fermi” Mantova

School Year 2011-2012

Physics course

The physics of sound

Many phenomena are concerned with wave motion: earthquakes, water surfaces changes, light, TV broadcasting

and sound.

We call sound the longitudinal, elastic wave perceived by the human ear.

Sound needs an oscillating source: for example, a beaten tuning fork.

The physical property perturbed is the displacement of each particle of the medium relative to its equilibrium shape.

Another physical property perturbed is pressure.

Then, in the mathematical function that represents the wave motion:

z = A sin (2 (x/λ – t))

z can be either displacement or pressure.

But pressure has a maximum when there is no displacement, and vice versa.

High displacement Low displacement

We can say that the two functions have a relative phase of a quarter of a period. Otherwise, we can use the sin (sine)

function for S and the cos (cosine) function for P.

As sound propagates in a medium, whose molecules play the role of spring coils, it is called an elastic wave.

Sound doesn’t propagate in a vacuum. It does propagate in a medium (e.g. air, water, steel).

Air Vacuum

Sound No Sound

It is also classified as a mechanical wave, as opposed to electromagnetic ones, which have the

E and B fields as the z parameter.

Electromagnetic Waves

The minimum amplitude A that can be heard is about 10-10 m and 10-4 Pa. There is no maximum value: sound waves can have

catastrophic effects.

Displacement is oriented along the direction of propagation:

sound is a longitudinal wave.

The audible frequency range goes from 20 Hz to 20 kHz. Ultrasounds have higher frequencies (for example, they are

used in echography). Infrasounds have lower frequencies (for example, they are perceived by elephants).

< 20 Hz> 20000 Hz

The wave identity is given by its frequency, the same of the oscillating source:

different musical notes have different frequencies.

For example, this tuning fork (La) has a frequency of 440 Hz. The larger the frequency, the higher the sound. The smaller

the frequency, the lower the sound.

Speed depends on the medium: it is faster in solids, slower in gases. In gases, temperature

and pressure values are also important. It is possible to relate them with a mathematical function:

Speed of sound in an ideal gas

We have here some examples. A useful datum: in air, at a temperature of 20° C and a pressure of 1,0 atm, the speed of sound is 343 m/s.

Medium Speed of Sound at 20°C

Air 343 m/s

Helium 972 m/s

Fresh Water 1.482 m/s

Steel 5.960 m/s

As you know, v = λ. So, if the medium parameters change, the wavelength λ also changes, being constant.

Higher speed, longer wavelength

Lower speed, shorter wavelength

The propagation is symmetrical in the three directions: sound is a spherical wave.

All waves transport energy and momentum. Generalizing the harmonic motion equation, ET= (1/2) kA2, total wave energy is

proportional to squared amplitude. To double a sound amplitude, we need four times the energy value.

Then, if we consider the time necessary to propagate energy, we better speak about wave power. Since the wave is

spherical, it is important to know on which surface S the energy spreads.

S

Now, we introduce a new quantity: the intensity I=P/S, whose unit is Watt per squared meters

Because the surface increases with the squared distance d, while power is constant, the product I times squared distance, related to the sound wave, is constant. In any couple of points

of the wave front, I1d12=I2d2

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