### Theory:

Sound is a form of energy. It is transferred through the air or any other medium in the form of mechanical waves.

**What is meant by a mechanical wave**?

A mechanical wave is a disturbance, which propagates in a medium due to the repeated periodic motion of the medium particles from their mean position. The disturbance, which is caused by the vibrations of the particles, is passed over to the next particles. It means that the energy can be transferred from one particle to another as a wave motion.

**Characteristics of a wave**:

- In wave motion, only the energy is transferred, not the particles.
- The velocity of the wave motion is different from the velocity of the vibrating particle.
- For the propagation of a mechanical wave, the medium must possess inertia, elasticity, uniform density and minimum friction among the particles.

**Amplitude**:

The amplitude of a sound wave can be defined as the maximum displacement of the particles from their mean position due to the vibrations.

Time period:

The time taken for one complete oscillation of a sound wave is called the time period of the sound wave.

$\mathit{Time}\phantom{\rule{0.147em}{0ex}}\mathit{period}=\frac{1}{\mathit{Frequency}}$

**Frequency:**

The number of oscillations an object takes per second is called its frequency.

The SI unit of frequency is \(Hertz\) (\(Hz\)).

The SI unit of frequency is \(Hertz\) (\(Hz\)).

$\mathit{Frequency}=\frac{\mathit{Total}\phantom{\rule{0.147em}{0ex}}\mathit{number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{oscillations}}{\mathit{Total}\phantom{\rule{0.147em}{0ex}}\mathit{time}\phantom{\rule{0.147em}{0ex}}\mathit{taken}}$

**Speed of the sound**:

The speed of the sound is defined as the distance that sound travels in one second. The letter ‘\(v\)' stands for the speed of the sound.

It is mathematically represented as,

$v\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}n\mathrm{\lambda}$

where '\(n\)' is the frequency and '$\mathrm{\lambda}$' is the wavelength.

Distance travelled by the sound wave is found by,

$\mathit{Distance}(d)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\mathit{Number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{waves}\times \mathit{Wavelength}(\mathrm{\lambda})$

**Example**:

A sound has a frequency of \(60\) \(Hz\) and a wavelength of \(10\) \(m\). What is the speed of the sound?

**Solution**:

Frequency(\(n\)) = \(50\)\(Hz\)

Wavelength(\(λ\)) = \(10\)\(m\)

**To find**: Speed of the sound(\(v\))

We know the formula,

$v=n\mathrm{\lambda}$

By applying the values, we get

\(v\) \(=\) $60\xb710$

\(v\) \(=\) 600 $m/s$