Two sources of sound $S_{1}$ and $S_{2}$ produce sound waves of same frequency 660 Hz . A listener is moving from source $\mathrm{S}_{1}$ towards $\mathrm{S}_{2}$ with a constant speed $\mathrm{u} \mathrm{m} / \mathrm{s}$ and he hears 10 beats $/ \mathrm{s}$. The velocity of sound is $330 \mathrm{~m} / \mathrm{s}$. Then, $u$ equals:

(D) $2.5 \mathrm{~m} / \mathrm{s}$

(A) $15.0 \mathrm{~m} / \mathrm{s}$

(B) $10.0 \mathrm{~m} / \mathrm{s}$

(C) $5.5 \mathrm{~m} / \mathrm{s}$

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Waves & Sound

Two sources of sound

S_{1}

and

S_{2}

produce sound waves of same frequency 660 Hz . A listener is moving from source

S_{1}

towards

S_{2}

with a constant speed

um / s

and he hears 10 beats

/ s

. The velocity of sound is

330 m / s

. Then,

u

equals:

Answer: (D)

Moving between the sources, the listener hears one frequency raised and the other lowered by the Doppler effect. Approaching

S_{2}

he hears

f \frac{v + u}{v}

, and receding from

S_{1}

he hears

f \frac{v - u}{v}

. The beat rate is their difference,

f \frac{( v + u ) - ( v - u )}{v} = \frac{2 f u}{v} = 10

. Solving,

u = \frac{10 v}{2 f} = \frac{10 \times 330}{2 \times 660} = 2.5

m/s.

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option