Question

A cars initially at rest, 330m away from a stationary observer. It begins to move towards the observer with an acceleration of $1.1m{s}^{-2}$, sounding its horn continuously. 20 s later, the driver stops sounding the horn. The velocity of sound in air is $330m{s}^{-1}$. The observer will hear the sound of the horn for a duration of

• A. $20s$
• B. $21s$
• C. $20\frac{2}{3}s$
• D. $19\frac{1}{3}s$

Answer 1

The correct option is D $19\frac{1}{3}s$

Suppose the car starts to move and sound its horn at time $t_0$. The sound reaxhes the observe in $1$ second.

Therefore, the observer begins to hear sound the time,

$t_1=(t_0+1)sec$

Displacement of car in $20$ seconds $=\frac{1}{2}\times 1.1\times {20}^2=220$ metre

Therefore at time $t_2=(t_0+20)sec$, the horn is switched off and the car is $110m$ away from the observer.

The sound emitted by the horn at the instant it switched off will travel to the observer in further time $\frac{1}{3}sec$

Therefore, the observer stops hearing the sound at time,

$t_3=t_2+\frac{1}{3}sec$.

Thus, the observer hears the sound for a duration of $t=(t_3-t_1)$

$=[t_2+\frac{1}{3}-t_1]$

$=[t_0+20+\frac{1}{3}-(t_0+1\left)\right]$

$=19\frac{1}{3}$ second