Question

Two trains are approaching each other with the speed of 72km/h.The frequency of the whistle of one train as heard by passanger in other train is 700 Hz.Find:(i) the real frequncy of the whistle

Answer 1

The real frequency of the whistle = 1076.12 Hz

f = frequency of the whistle heard by the other train = 700 Hz

f' = real frequency of the whistle

Using the Doppler's effect equation to find the value of f'-

f' = f (velocity of sound w.r.t listener / velocity of sound w.r.t to source)

velocity w.r.t listener = speed of sound in air + speed of train

= 340 + 72 = 412 m/s (taking speed of sound as 340 m/s)

velocity w.r.t source = speed of sound in air - speed of train

= 340 - 72 = 268 m/s (taking speed of sound as 340 m/s)

f' = 700 × (412/268)

f' = 1076.12 Hz

The original frequency of the whistle = 1076.12 Hz

Answer 2

The real frequency of the whistle is 775.8 Hz.

Explanation:

Given that,

Frequency = 700 Hz

Speed of source= 72 km/h =20 m/s

Suppose, Two trains are approaching each other with the speed of 72 km/h and 54 km/h relative to the ground. find the real frequency of the whistle before the trains meet.

Speed of observer = 54 km/h = 15 m/s

We need to calculate the real frequency of the whistle

Using formula of frequency

$f'=f\times(\dfrac{v+v_{0}}{v-v_{s}})$

Put the value in to the formula

$f'=700\times(\dfrac{343+15}{343-20})$

$f'=775.8\ Hz$

Hence, The real frequency of the whistle is 775.8 Hz.

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Topic : frequency

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