Question

Two sinusoidal sound waves were generated from same source after a time gap of 2 sec what is the phase difference between them if their time period is 10s.

• A. $\pi$
• B. $\frac{\pi }{2}$
• C. $\sqrt{3}\frac{\pi }{2}$
• D. $\frac{2\pi }{5}$

Answer 1

The correct option is D

$\frac{2\pi }{5}$

In one time period a wave can travel $\lambda$ distance or one wavelength unitary method

$T-\lambda$

$1-\frac{\lambda }{T}$

$2-\frac{2\lambda }{T}$

so first wave that originated 2 sec before second wave will have a lead $\frac{2\lambda }{T}$

$\Rightarrow △x=\frac{2\lambda }{T}$

$△\varphi =\frac{2\pi }{\lambda }△x$

=$\frac{2\pi }{\lambda }\frac{2\lambda }{T}=\frac{4\pi }{T}$

=$\frac{4\pi }{10}=\frac{2\pi }{5}$