A train is moving on a straight track with speed 20 m s⁻¹. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 m s⁻¹ ) close to:
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Question

A train is moving on a straight track with speed 20 m s⁻¹. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 m s⁻¹ ) close to:

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G1 Physics · Accepted Answer

Step 1: Just before passing, f₁=fv/(v−vₛ); just after passing, f₂=fv/(v+vₛ). Step 2: With v=320 and vₛ=20 m s⁻¹, f₁≈1066.7 Hz and f₂≈941.2 Hz. Relative change ≈(f₁−f₂)/1000≈12.5%. Closest option: 12%, B.