Question

Two sources are at a finite distance apart. They emit sound of wavelength $\lambda$. An observer situated between them on line joining the sources, approaches towards one source with speed u, then number of beats heard per second by observer will be

• A. $\frac{2u}{\lambda}$
• B. $\frac{u}{\lambda}$
• C. $\frac{u}{2\lambda}$
• D. $\frac{2\lambda}{u}$

Answer 1

Answer: (A)

$ n_1= \bigg( \frac{v + u}{v }\bigg)n$ and $ n_2= \bigg( \frac{v - u}{v }\bigg)n$
Number of beats per second
$ x = n_1 -n_2= \bigg( \frac{v + u}{v }\bigg)n- \bigg( \frac{v - u}{v }\bigg)n$
$ = \bigg( \frac{v + u - v+u}{v }\bigg)n$
$ = 2u\bigg( \frac{n}{v }\bigg)= \frac{2u}{\lambda}$