Question

A longitudinal wave travels at a speed of $0.3m{{s}^{-1}}$and the frequency of the wave is 20 Hz. Find the separation between the two consecutive compressions.

Answer 1

Hint: Separation between two consecutive compressions refers to its wavelength and can be calculated by the relation between velocity, frequency and speed.

Formula used:
 \[v=\lambda \times \nu \]
Where,
$\lambda $= wavelength of wave,
v=speed of wave,
\[\nu \]=frequency of wave.

Complete step-by-step answer:
According to question v= $0.3m{{s}^{-1}}$ and \[\nu \]=20 Hz

Putting in formula \[v=\lambda \times \nu \] we get,

\[\begin{align}
  & 0.3=\lambda \times 20 \\
 & \lambda =\dfrac{0.3}{20} \\
 & \lambda =\dfrac{3}{200} \\
 & \lambda =0.015\,m \\
\end{align}\]

Therefore, separation between two consecutive compressions which is equal to its wavelength is 0.015m.

Additional Information:
Wave is basically transport of energy without transport of its matter. It can also be described as a disturbance that travels through medium. A wave is a physical phenomenon characterized by its frequency, amplitude and wavelength. Waves are made up of compressions and rarefactions. Compression is known as the position in which particles are closest to each other whereas rarefaction is its complete opposite, it is a position in which the particles are farthest from each other.

Note: Often students think that the distance between two compressions refers to twice its wavelength and multiply the answer by 2. However, distance between two compressions as well as rarefactions refer to its wavelength.