Question

A car running with a velocity $30m/s$ reaches midwway between two vertical parallel walls separated by $360m$,when the driver sounds the horn for a moment.Speed of sound in air is $330m/s$.After blowing horn ,the first three echoes will be heard by the driver respectively at _____.

• A. $1.2s,2.4s,3.0s$
• B. $1.0s,2.4s,3.0s$
• C. $1.0s,2.0s,3.0s$
• D. $1.2s,2.4s,3.6s$

Answer 1

The correct option is C $1.0s,2.0s,3.0s$

$\text{Let the first echo heard after}{t}_1\text{second:}$

$\text{in}{t}_1\text{second, distance traveled by the car}=v\ast t_1=30t_1$

distance traveled by sound for first echo$=d-30t_1{v}_s\ast t_1=360-30t_{1}330\ast t_1=360-30t_{1}360t_1=360t_1=1sec$

$\text{Let the second echo heard after}{t}_2\text{second:}$

$\text{in}{t}_2\text{second, distance traveled by the car}=v\ast t_2=30t_2$

distance traveled by sound for second echo$=2d-30t_2{v}_s\ast t_2=2\ast 360-30t_{2}330\ast t_2=720-30t_{2}360t_2=720t_2=2sec$

$\text{Let the third echo heard after}{t}_3\text{second:}$

$\text{in}{t}_3\text{second, distance traveled by the car}=v\ast t_3=30t_3$

distance traveled by sound for third echo$=3d-30t_3{v}_s\ast t_3=3\ast 360-30t_{3}330\ast t_3=1080-30t_{3}360t_3=1080t_3=3sec$

$t_1,t_2,t_3=1sec,2sec,3sec$