Istituto “Enrico Fermi” Mantova School Year 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). AirVacuum 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 m and 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 > 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. MediumSpeed of Sound at 20°C Air343 m/s Helium972 m/s Fresh Water1.482 m/s Steel5.960 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, E T = (1/2) kA 2, 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, I 1 d 1 2 =I 2 d 2 2.

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