A train sounds its whistle as it approaches an observer standing at a point near the track.The observer measures a frequency of 216 Hz as the train approaches and a frequency of 184 Hz as the train leaves.What is the frequency of its whistle?
Answers
frequency of its whistle is 198.72 Hz
when the train approaches, frequency heard by observer, f = f₁(v/v - vs)
⇒216 = f₁(340/340 - vs)............(1)
when train leaves, frequency heard by observer
f' = f₁(v/v+ vs)
⇒184 = f₁(340/340 + vs) ...........(2)
from equations (1) and (2) we get,
216/184 = (340 + vs)/(340 - vs)
⇒vs = 136/5 = 27.2 m/s
now 216 = f₁(340/340 - 27.2)
⇒216 × 312.8/340 = f₁
⇒f₁ = 198.72 Hz
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when the train approaches, frequency heard by observer, f = f₁(v/v - vs)
⇒216 = f₁(340/340 - vs)............(1)
when train leaves, frequency heard by observer
f' = f₁(v/v+ vs)
⇒184 = f₁(340/340 + vs) ...........(2)
from equations (1) and (2) we get,
216/184 = (340 + vs)/(340 - vs)
⇒vs = 136/5 = 27.2 m/s
now 216 = f₁(340/340 - 27.2)
⇒216 × 312.8/340 = f₁
⇒f₁ = 198.72 Hz