question_answer

Two sources are at a finite distance apart. They emit sounds of wavelength \[\lambda \]. An observer situated between them on line joining approaches one source with speed u. Then the number of beats heard/s by observer will be: [AIPMT 2000]

A)              \[\frac{2u}{\lambda }\] 

B)                   \[\frac{u}{\lambda }\]

C)              \[\frac{u}{2\lambda }\] 

D)                   \[\frac{\lambda }{u}\]

Correct Answer: A

Solution :

Let v be the speed of sound and n the original frequency of each source.

They emit sounds of wavelength \[\lambda \]

When observer moves towards one source (say A), the apparent frequency of A as observed by the observer will be

\[n'=n\left( \frac{v+u}{v} \right)\]

The observes is now receding source B, so die apparent frequency of S observed will be

\[n'=n\,\left( \frac{v-u}{v} \right)\]

Thus, number of beats

but

Thus,