Question

Distance between a compression and rarefaction is 100m. Calculate the wavelength of the wave:
A. 100 m
B. 50 m
C. 200 m
D. 400 m

Answer 1

Hint: As we know that the wavelength of any longitudinal wave is the distance between two consecutive compression or the distance between two consecutive rarefactions, and also, we know that in any wave the compression and rarefaction occur alternately.

Complete answer:
Wavelength= distance between two consecutive compression.
And also, we can write the wavelength in the terms of the rarefaction as follows,
Wavelength= distance between two consecutive rarefactions.
And also, we know that the rarefaction and the compressions occur alternately then we can also write like,
Wavelength= 2(distance between compression and rarefaction)
And we have given with the value of distance between compression and rarefaction= 100m
So, the wavelength of the wave= \[2 \times 100 = 200m\]
So, the wavelength of the wave is $200m$.

So, the correct answer is “Option C”.

Note:
In any longitudinal wave we will find compression and rarefaction both, so we should understand properly what are the compression and rarefactions of a longitudinal wave. When the wave propagates then the particles in it will settle themselves differently. In some regions the particle will be closer while in some regions the particle will be far.
So, in a longitudinal wave the compression is the region where the patties are the closest together while the rarefaction in a longitudinal wave is the region where particles are farthest apart from each other. The sound wave and ultrasound wave are examples of some longitudinal waves which we will encounter in our day to day life.