Two sources are at a finite distance apart. They emit sound of wavelength $\lambda$. An observer situated…
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 [UP CPMT 2011]
$\frac{2u}{\lambda}$
$\frac{u}{\lambda}$
$\frac{u}{2\lambda}$
$\frac{\lambda}{u}$
Solution
As, $n_1 = \left(\frac{v + u}{v}\right) n$ and $n_2 = \left(\frac{v - u}{v}\right) n$
Number of beats per second,
$x = n_1 - n_2 = \left(\frac{v + u}{v}\right) n - \left(\frac{v - u}{v}\right) n$
$= \left(\frac{v + u - v + u}{v}\right) n = 2u \left(\frac{n}{v}\right) = \frac{2u}{\lambda}$