Question

A car is initially at rest, 330 m away from a stationary observer. It begins to move towards the observer with an acceleration of 1.1 m/s² , sounding its horn continuously. 20 second later, the driver stops sounding the horn. The velocity of sound in air is 330 m/s. The observer will hear the sound of the horn for a duration of:

(A) 20 sec 

(B) 21 sec 

(C) 62/3 sec 

(D) 58/3 sec

Answer 1

Correct option: (D) 58/3 sec

Explanation:

In 20 seconds , distance travelled by the Source is : 

S = 1/2  (1.1) (20)² = 220 m. 

Let, t = 0 be the starting time. 

The sound wave started at t = 0 from 'A' reaches the observer at 'B' after(330/330) = 1sec. ie. observer started hearing the sound at t = 1 sec. At t = 20 sec. the source reaches at 'C' 220 m from 'A'.

The last sound wave starting from 'C' reaches 'B' after (110/330) = 1/3 sec < 1 sec.

  Hence , the observer do not hear the sound for whole 20 sec. but for: