### Theory:

A sound wave can be explained completely by five characteristics; they are

- Amplitude
- Frequency
- Time period
- Wavelength
- Velocity or speed

*Wave nature*

**Amplitude (\(A\))**:

The wave's amplitude is the maximum displacement of medium particles from their original undisturbed positions when a wave passes through the medium. The sound will be loud if the vibration of a particle has a large amplitude and soft if the vibration has a small amplitude. 'A' stands for amplitude. The \(metre\) \(m\) is its SI unit.

Time period (\(T\)):

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 (\(F\)):**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 \(Hertz\) (\(Hz\)).

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

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

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 \(70\) \(Hz\) and a wavelength of \(10\) \(m\). What is the speed of the sound?

**Solution:**

Frequency (\(n\)) \(=\) \(70\) \(Hz\)

Wavelength (\(λ\)) \(=\) \(10\) \(m\)

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

We know the formula,

$v=n\mathrm{\lambda}$

By applying these values we get,

\(v\) \(=\) $70\xb710$

\(v\) \(=\) 700$m/s$