First slide

Doppler

Question

Two sources A and B are sounding notes of frequency 680 Hz. A listener moves from A to B with a constant velocity u. If speed of sound is 340 $m s^{- 1}$ , what should be the value of u so that he hears 10 beats/s ?

Moderate

A

$2.0 m s^{- 1}$
B

$3.0 m s^{- 1}$
C

$2.5 m s^{- 1}$
D

$3.5 m s^{- 1}$

Solution

$\overset{A}{S_{1}} \underset{U}{\to} \overset{B}{S_{2}}$
He is approaching $S_{2}$
$n_{2} = (\frac{u + u_{o}}{u}) n$
And going away from $S_{1}$
$\begin{array}{l} n_{1} = (\frac{u - u_{o}}{u}) n \\ n_{2} - n_{1} = 10 \end{array}$
$(\frac{u + u_{o}}{u}) n - (\frac{u - u_{o}}{u}) n = \frac{2 u_{o} n}{u} = 10$
$u_{o} = \frac{10 \times 340}{2 \times 680} = 2.5 m / s$

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