### 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 $$Hertz$$ ($$Hz$$).
$\mathit{Frequency}=\frac{\mathit{Total}\phantom{\rule{0.147em}{0ex}}\mathit{number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{oscillations}}{\mathit{Total}\phantom{\rule{0.147em}{0ex}}\mathit{time}\phantom{\rule{0.147em}{0ex}}\mathit{taken}}$

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,

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

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,

$$v$$ $$=$$ $70·10$

$$v$$ $$=$$ 700$m/s$