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 the 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{\lambda }{u} $

Answer 1

Answer: (A)

$ {{n}_{1}}=\left( \frac{v+u}{v} \right)n $ and $ {{n}_{2}}=\left( \frac{v-u}{v} \right)n $ Number of beats per second $ x={{n}_{1}}-{{n}_{2}} $ $ =\left( \frac{v+u}{v} \right)n-\left( \frac{v-u}{v} \right)n $ $ =\left( \frac{v+u-v+u}{v} \right)n $ $ =2u\left( \frac{n}{v} \right)=\frac{2u}{\lambda } $