What is the wavelength of a longitudinal wave if the distance between the $5th$ rarefaction and $6th$ rarefaction is $25\,cm$ ?
A. $25\,cm$
B. $50\,cm$
C. $40\,cm$
D. $20\,cm$

Hint: In order to solve this question we need to understand sound waves and its propagation. Sound waves are longitudinal waves, which requires a material medium to propagate. It propagates with compression and rarefaction. Actually when an atom vibrates then it strikes the neighboring atom and this process continues, the pattern of vibration is recognized as sound. So when two atoms are close to each other while vibrating it is known as compression and when the two atoms are at extreme far distance from each other while vibrating, it is known as rarefaction.

Complete step by step answer:
Wavelength of a wave is defined as the distance between two consecutive crests or between two consecutive troughs of wave, so for a longitudinal wave compression is trough and rarefaction is crest of wave.So wavelength is defined as distance between two consecutive distance between two compressions or between two consecutive rarefaction of wave.So according to problem distance between $5th\,\&\, 6th$ rarefaction is $25\,m$.So the wavelength is $\lambda = 25\,cm$.

So the correct option is A.

Note: It should be remembered that waves are known as disturbance in medium.There are two types of wave, one is longitudinal wave and other is transverse wave.Longitudinal waves are those waves in which wave propagation direction is direction in which vibration happens like sound waves, but transverse waves are those waves in which displacement of vibration is perpendicular to wave propagation direction.