Question

The phase difference between two points is $\pi /3$. If the frequency of wave is 50 Hz, then what is the distance between two points? (given v = 330 m/s)

• A. 2.2 m
• B. 1.1 m
• C. 0.6 m
• D. 1.7 m

Answer 1

The correct option is B 1.1 m

Phase difference $=\frac{2\pi }{\lambda }\times$path difference.
The phase difference between any two particles in a wave determines lack of harmony in the vibrating state of two particles ie, how far one particle leads the other or lags behind the other.
From relation
$\Delta \varphi =\frac{2\pi }{\lambda }\times \delta x$

$\Rightarrow \Delta x=\frac{\lambda }{2\pi }\times \Delta \varphi$ ...(i)

Also, $\lambda =\frac{v}{n}$ ...(ii)
Now, from Eqs. (i) and (ii), we get
$\Delta x=\frac{v}{2\pi n}\times \Delta \varphi$

$\Rightarrow \Delta x=\frac{330}{2\pi \times 50}\times \frac{pi}{3}$
or $\Delta x=1.1m$