Question

An echo returned in 3 s. What is the distance of the reflecting surface from the source, given that the speed of sound is 342m${s^{ - 1}}$?
(A) 520 m
(B) 515 m
(C) 530 m
(D) 513 m

Answer 1

The speed of sound and the echo time is used to evaluate the location of the reflecting surface using the distance-time formula.

Complete step by step solution:
Given that the speed of sound, v=342m${s^{ - 1}}$
And time taken for the echo to return, t=3s
We know that, Distance = velocity$\times$time=$342 \times 3 = 1026m$
The above value is the distance travelled by the echo from the source to the reflecting surface and back to the source.
But, we have been asked to calculate the distance of the reflecting surface from the source, which is half the value of the distance calculated above.
So, distance of reflecting surface from source=$\dfrac{{1026}}{2} = 513m$

The correct option is D.

Note: The speed of sound is the propagation speed of the sound waves in a medium. Typically, the sound waves reflect on any surface on which it is incident. The reflected sound waves reaching the sources would result in echo. Typically surfaces also absorb the sound waves. Echo can be both beneficial and undesirable. In the music recording and in the cinema halls the echo becomes an unwanted effect, and these are prevented by using sound absorbing material on the walls. However, there are scientific and medical applications where the echoing is found to be very useful. One of the major applications include the SONAR imaging in submarines, where the sound waves are emitted under the water and the reflected waves from the objects are detected to calculate the distance of the underground object from the submarine. In medical applications, sound waves of very high frequencies known as ultrasound are used to image the organs and the tissue in the human body.