Question

Two sound sources emitting sound each of wavelength $\lambda$ are fixed at points $A$ and $B.A$ listener moves with velocity u from $A$ to $B$. The number of beats heard by him per second is

• A. $\frac{2u}{\lambda }$
• B. $\frac{u}{\lambda }$
• C. $\frac{u}{3\lambda }$
• D. $\frac{2\lambda }{u}$

Answer 1

Answer: (A)

The observed frequency from $A$,
${\upsilon }_A=\frac{\upsilon ({\upsilon }_s-u)}{{\upsilon }_s}$
where ${\upsilon }_s$ is the velocity of sound The observed frequency from $B$,
${\upsilon }_B=\frac{\upsilon ({\upsilon }_s-u)}{{\upsilon }_s}$
$\therefore$ Number of beats per second
$={\upsilon }_B-{\upsilon }_A=2\frac{\upsilon }{{\upsilon }_s}u=\frac{2u}{\lambda }$