Question

A sound wave in air has a frequency of 282 Hz and travels with a speed of 343 m/s. How far apart are the wave crests (compressions)?

Short answer

The wave crests (compressions) are $1.22\mathrm{m}$apart.

Step-by-step solution

Understanding the wave speed of sound wave

The sound wave is a wave of the crest (compression) and trough (rarefaction), by which sound is propagated in an elastic medium such as air. The wave speed is the speed at which the crest or trough of the wave moves forward.

Identification of the given information

The frequency of the sound wave in air is, $f=282\mathrm{H}\mathrm{z}$.

The speed of the sound wave in air is, $v=343\mathrm{m}/\mathrm{s}$.

Determination of the distance between the wave crests  

The expression for the wavelength of the wave can be written as:

$\lambda =\frac{v}{f}$

On substituting the given values of v and f in the above expression, you will get:

$\begin{array}{rl}c\lambda & =\frac{343\mathrm{m}/\mathrm{s}}{282\mathrm{H}\mathrm{z}}\\ & =1.22\mathrm{m}\end{array}$

The distance between the two wave crests is termed as the wavelength of the wave. Thus, the distance between the wave crests is 1.22 m.