Question

18.
The speeds of sound in air and sea-water are given to be 340
m/s and 1440 m/s. respectively. A ship sends a strong Signal
straight down and detects its echo after 1.5 secs. The depth
of the sea at that point is
Delhi 2012]
(1) 2.16 km
(2) 1.08 km
(3) 0.51 km
(4) 0.255 km ​

Answer 1

Answer:

Speed of Sound in air = 340 m/s

Speed of Sound in sea water = 1440 m/s

Time taken for echo to be received = 1.5 seconds

We know that, Distance is Speed × Time. Here we know the speed of sound and the time taken for the sound wave to complete 1 cycle of echo.

In the case of echo, the sound wave first travels and hits the surface of the ground. Later it travels the same distance and comes back to the detector present in the ship. Therefore it is covering the distance two times. But since we require only the depth, we only calculate the distance once.

Therefore in terms of formula we can represent it as:

⇒ 2d = s × t

⇒ 2d = 1440 m/s × 1.5 s

⇒ 2d = 2160 m

⇒ d = 2160/2 = 1080 m

Therefore the depth of the sea is 1080 m or 1.08 km.

Answer 2

$\huge \star \mathbb\green{ \bigstar \: hello \: mate \bigstar} \star$

Speed of Sound in air = 340 m/s

Speed of Sound in sea water = 1440 m/s

Time taken for echo to be received = 1.5 seconds

TIME = 1.5 SEC

We know that ,

$\tt{dsitance \: = speed \times time}$

Here we know the speed of sound and the time taken for the sound wave to complete 1 cycle of echo.

$\tt \boxed{what \: is \: echo \implies}$

An echo is a sound that is repeated because the sound waves are reflected back.

In the case of echo, the sound wave first travels and hits the surface of the ground.

Later it travels the same distance and comes back to the detector present in the ship.

Therefore it is covering the distance two times.

But since we require only the depth, we only calculate the distance once.

Therefore in terms of formula we can represent it as:

$\implies \tt{2d \: = speed \: \times time}$

$\implies \tt{2d \: = \: 1440 \: m/s \: × 1.5 s}$

$\implies \tt{2d = 2160 m} \\ </p><p> \\ \implies \tt{ d = \frac{2160}{2} = 1080 m}$

Therefore the depth of the sea is 1080 m or 1.08 km.