Question

An oil tanker explodes in the sea. At that instant an aircraft and a submarine were present vertically above and below the oil tanker respectively at equal distances from it. Find the ratio of the time taken by sound waves to reach them. (Speed of sound in air = $320m{s}^{-1}$. Speed of sound in sea water = $1520m{s}^{-1}$)

• A. 17 : 8
• B. 15 : 9
• C. 18 : 5
• D. 19 : 4

Answer 1

The correct option is D 19 : 4

Given:
Speed of sound in air, $v_a=320m{s}^{-1}$
Speed of sound in water, $v_w=1520m{s}^{-1}$

Let the aircraft and the submarine be $xm$ above and below the tanker respectively.

Speed is given as the ratio of distance and time.
Hence, time taken by sound to reach the aircraft is:
$t_a=\frac{x}{v_a}$
Time taken by sound to reach the submarine is:
$t_w=\frac{x}{v_w}$

Ratio of the times is:
$n=\frac{t_a}{t_w}$
$n=\frac{x/320}{x/1520}$
$n=\frac{1520}{320}=\frac{19}{4}$

Therefore the ratio is 19 : 4.