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Question

Physics Question on Waves

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

A

2uλ\frac{2u}{\lambda }

B

uλ\frac{u}{\lambda }

C

u2λ\frac{u}{2\lambda }

D

λu\frac{\lambda }{u}

Answer

2uλ\frac{2u}{\lambda }

Explanation

Solution

n1=(v+uv)nn_{1}=\left( \frac{v +u}{v} \right)n and n2=(vuv)nn_{2}=\left( \frac{v-u}{v} \right)n Number of beats per second x=n1n2x=n_{1}-n_{2} =(v+uv)n(vuv)n=\left( \frac{v +u}{v} \right)n-\left( \frac{v-u}{v} \right)n =(v+uv+uv)n=\left( \frac{v+ u -v +u}{v} \right)n =2u(nv)=2uv=2u \left( \frac{n}{v} \right)=\frac{2u}{v}