Question

Two stationary sources each emitting waves of wave length $λ$. An observer moves from one source to other with velocity $u$. Then number of beats heard by him:

• A. $\frac{2u}{λ}$
• B. $\frac υλ$
• C. $\sqrt {uλ}$
• D. $\frac {υ}{2λ}$

Answer 1

Answer: (A)

$\frac{2u}{λ}$

Answer 2

$For \ first \ source$

$n_1=n(\frac {v-u}{v})=(1-\frac {u}{v})n$

$For \ second\ source$

$n_2=n(\frac {v+u}{v})=(1+\frac {u}{v})n$

$Beat\ freq.=|n_1-n_2|$

$Beat\ freq.$ $=$ $n+\frac {nu}{v}-n+\frac {nu}{v}$

$Beat\ freq.$ =$$\frac {2nu}{v}

$Beat\ freq.$ $=$ $\frac {2u}{λ }$ $[∵v=nλ, \ ∴\frac 1λ=\frac {n}{v}]$

So, the correct option is (A): $\frac{2u}{λ}$