Question

A car driving at a constant speed of 25 $m/s$, heads straight to a mountain. The driver presses the car horn and recieves an echo 3.6 seconds later. Calculate the distance between the car and the mountain when the driver pressed the horn.

(An echo is a repeated sound that is caused by the reflection of the sound waves from the surface. Take the speed of sound in air to be 300 $m/s$. )

• A. 1080 m
• B. 90 m
• C. 585 m
• D. 495 m

Answer 1

The correct option is C 585 m

Given,
Speed of the car, S = 25 m/s
Speed of the sound in air, V = 300 m/s
Time taken to receive the echo, T = 3.6 s

Let the distance between the car and the mountain when the driver pressed the horn be X.
Let the distance between the car and the mountain when the driver recieved the echo be Y.


After 3.6 seconds, the distance travelled by the car = X - Y
Therefore, X - Y = S $\times$ T
= 25 $\times$ 3.6 = 90 m ...............(i)
Distance travelled by the sound wave from the horn pressed till the echo recieved by the driver = X + Y
Therefore, X + Y = V $\times$ T
= 300 $\times$ 3.6 = 1080 m .................(ii)

From (i) and (ii),
X - Y = 90
X + Y = 1080
Therefore, by solving (i) and (ii),
2X = 1170
X = 585

Hence, the distance between the car and the mountain when the driver pressed the horn is 585 m.