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 -2 , sounding its continuously. 20 later, the driver stops sounding the **. The velocity of sound in air is 330 m -1 . The observer will hear the sound of the *** for a duration of

(a) 20 *

(b) 21 *

(c) 20 2/3 *

(d) 19 1/3 *

Answer 1

Correct Answer is: (a) 20 s

Let the car begin to move and sound its **** at time t0.

The sound reaches the observer in 1 *.

∴ the observer begins to hear the sound at time t1 = t0 + 1 *.

The displacement of the car in 20 is (1/2) (1.1 m -2) (20 *)2 = 220 m.

∴ at time t2 = t0 + 20 , the is switched and the car is 110 m away from the observer. The sound emitted by the ** at the instant it is switched will travel to the observer in a further time (1/3) .

∴ the observer stops hearing the sound at time t3 = t2 + 1/3 *.

∴ the observer hears sound for a duration of

t = t3 - t1 = t2 + 1/3 - t1 = (t0 + 20 ) + 1/3 - (t0 + 1 ) = 19 1/3 *.