IIT-JEE 2007 · Paper 2 · Physics Q14

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PhysicsSingle correct+4 / -1Question 14 of 66

Passage

Paragraph for Question Nos. 14 to 16

Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle.

Assume that the sound of the whistle is composed of components varying in frequency from $f_1=800$ Hz to $f_2=1120$ Hz, as shown in the figure. The spread in the frequency (highest frequency − lowest frequency) is thus 320 Hz. The speed of sound in still air is 340 m/s.

(Figure: intensity against frequency, a flat-topped band from $f_1$ to $f_2$ .)

(The paragraph is not printed in the official archive copy (which reproduces only the questions with their answers); its text is restored from the JEE 2007 question paper.)

The speed of sound of the whistle is

340 m/s for passengers in A and 310 m/s for passengers in B

360 m/s for passengers in A and 310 m/s for passengers in B

310 m/s for passengers in A and 360 m/s for passengers in B

340 m/s for passengers in both the trains

Answer and worked solution

Official answer: B

Relative to the air sound moves at 340 m/s in every direction.

Passengers in A are behind the engine, so the sound travels backwards to them while the train moves forward at 20 m/s: relative speed $340+20=360$ m/s.
Passengers in B are ahead; the sound moves forward and B moves away at 30 m/s: $340-30=310$ m/s.

(B)

Topics:Speed of waves Relative velocity

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IIT-JEE 2007 · Paper 2, Physics question 14