Question

The linear distance between the compression and the adjacent rarefaction is $0.8m$. The wavelength of the longitudinal wave is
(A) $0.8m$
(B) $1.6m$
(C) $0.4m$
(D) $3.2m$

Answer 1

Hint: Here we are provided with the distance between the successive compression and rarefaction. The wavelength of a wave is the distance between any two successive compressions or rarefactions. So the given value is half of the wavelength. Hence we can find the wavelength by multiplying it by 2.

Complete step by step answer:
From the definition of the wavelength of a wave we get to know that the wavelength is the distance between two successive compressions or two successive rarefactions of a wave.
Here in the question, we are given the distance between the compression and rarefaction. The wave moves forward by continuous successive compression followed by a rarefaction.
So this distance is half the wavelength of a wave.
therefore,
$\Rightarrow \dfrac{\lambda }{2} = 0.8m$
So to find the wavelength, we multiply the 2 on both sides and get,
$\Rightarrow \lambda = 0.8 \times 2m$
Hence we get the value of wavelength as,
$\Rightarrow \lambda = 1.6m$
Therefore, the wavelength of the wave is $\lambda = 1.6m$
The correct option is (B); $1.6m$.

Additional Information
In the case of light, the wavelength varies with the colour. The red coloured light has the longest wavelength and the violet coloured light has the shortest wavelength. The wavelength is also inversely proportional to the frequency, which means that the longer is the wavelength, the less is the frequency of the light.

Note:
The compressions of a wave are generally the regions of high pressure while the rarefactions are the regions with low pressure. The wavelength in such a case is defined as the distance the disturbance travels in one complete cycle of the wave.