Question

The wavelength of a wave in medium is $0.5m$. Due to this wave the phase difference between the two particles of the medium is ${\pi \mathord{\left/ {\vphantom {\pi 5}} \right.} 5}$. The minimum distance between these points is
(A) 5 km
(B) 5 m
(C) 5 mm
(D) 5 cm

Answer 1

Hint
For a whole wavelength the phase difference between two particles is $2\pi$. So for a small phase difference as given in the question, the distance between the two particles can be found by using the wavelength of the wave.

Complete step by step answer
The wavelength of a wave is the distance between two identical points on a wave, like the distance between two peaks or the distance between two crests. It is usually specified in the units of length. For a wave of a given wavelength $\lambda$, for the particles having a distance of $\lambda$ in between them, the phase difference is given by $2\pi$. In the question, we are said that the two particles have a phase difference of ${\pi \mathord{\left/ {\vphantom {\pi 5}} \right.} 5}$.
So we can write,
When the phase difference is $2\pi$ the distance between the two particles is given by $\lambda$. Therefore when the phase difference is ${\pi \mathord{\left/ {\vphantom {\pi 5}} \right.} 5}$, then the distance between the particles should be given by,
$\dfrac{\lambda }{{2\pi }} \times \dfrac{\pi }{5}$
So cancelling the $\pi$ from the numerator and the denominator, we get
$\dfrac{\lambda }{{2 \times 5}} = \dfrac{\lambda }{{10}}$.
In the given question, the value of $\lambda$ is $0.5m$.
So substituting this value, we get the phase difference as,
$\dfrac{{0.5}}{{10}}m$
That is $0.05m$. So we can write this in cm as, $0.05m = 5cm$
So the correct option will be D; 5cm.

Note
The wavelength of a wave is a distance over which the shape of a wave repeats. For a sinusoidal wave moving at constant wave speed, the wavelength of the wave is inversely proportional to the frequency. The path difference between two particles in a wave is the physical distance between the two points.