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 $1.1m{s}^{-2}$, 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. 20 s
• B. 21 s
• C. $20\frac{2}{3}s$
• D. $19\frac{1}{3}s$

Answer 1

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

Supposing the cars start moving and its horn sounds at time $t_o$.

The time in which the sound reaches the observer=1 second

$t_1=(t_o+1)$ sec

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

$t_2=(t_o+20)$ sec

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

Thus, the observer hears the sound for a duration of t=$(t_3-t_1)=[t_2+\frac{1}{3}-t_1]=[t_o+20+\frac{1}{3}-(t_o+1\left)\right]=19\frac{1}{3}s$