If a source approaches and recedes from observer with same velocity, the ratio of frequencies (apparent) is 6: 5, then velocity of source is: (vs=330 m/s)

Question

If a source approaches and recedes from observer with same velocity, the ratio of frequencies (apparent) is 6: 5, then velocity of source is: (vs=330 m/s)  (A) 20 m/s (B) 10 m/s (C) 30 m/s (D) 33 m/s

Tardigrade Admin · Accepted Answer

From Dopplers/effect, the perceived frequency when source approaches observer is

n = n (\frac{v}{v - v _{s}})

..(i)
When source recedes the observer

= n

= n (\frac{v}{v + v _{s}})

..(ii)
From Eqs. (i) and (ii), we get

\frac{n}{n} = \frac{v + v _{s}}{v - v _{s}}

\frac{6}{5} = \frac{330 + v _{s}}{330 - v _{s}}

\Rightarrow 1980 - 6 v_{s} = 1650 + 5 v_{s}

\Rightarrow 11 v_{s} = 1980 - 1650 = 330

v_{s} = \frac{330}{11} = 30 m / s

Q. If a source approaches and recedes from observer with same velocity, the ratio of frequencies (apparent) is 6:5, then velocity of source is: (vs​=330m/s)

20 m/s

10 m/s

30 m/s

33 m/s

Q. If a source approaches and recedes from observer with same velocity, the ratio of frequencies (apparent) is $6 : 5$ , then velocity of source is: $(v_{s} = 330 m / s)$