Two sources are at a finite distance apart. They emit sound of wavelength λ. 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

Question

Two sources are at a finite distance apart. They emit sound of wavelength λ. 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) (2u/λ) (B) (u/λ) (C) (u/2λ) (D) (2λ/u)

Tardigrade Admin · Accepted Answer

n1= ( (v + u/v ))n and n2= ( (v - u/v ))n Number of beats per second x = n1 -n2= ( (v + u/v ))n- ( (v - u/v ))n = ( (v + u - v+u/v ))n = 2u( (n/v ))= (2u/λ)

Q. Two sources are at a finite distance apart. They emit sound of wavelength $λ$ . 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

$\frac{2 u}{λ}$

$\frac{u}{λ}$

$\frac{u}{2 λ}$

$\frac{2 λ}{u}$

$n_{1} = (\frac{v + u}{v}) n$ and $n_{2} = (\frac{v - u}{v}) n$
Number of beats per second
$x = n_{1} - n_{2} = (\frac{v + u}{v}) n - (\frac{v - u}{v}) n$
$= (\frac{v + u - v + u}{v}) n$
$= 2 u (\frac{n}{v}) = \frac{2 u}{λ}$

Q. Two sources are at a finite distance apart. They emit sound of wavelength λ. 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

λ2u​

λu​

2λu​

u2λ​