Question

The splash is heard after 4.22 sec after the stone is dropped into a well of depth 78.4 m .the velocity of sound is?

Answer 1

Let the velocity of sound be v. Time taken by stone to reach bottom of well be t.

We have:

-78.4=0t-1/2*9.8*t2

t=4 s

 

Time taken by sound to reach top,t'=4.22-4=0.22 s

Hence,

Speed of sound,v=78.4/0.2556.36.2=356.36 ms-1

Answer 2

Answer:

v = 356.36 m/s

Explanation:

It is given that,

The stone is dropped into a well of depth 78.4 m

The splash is heard after 4.22 seconds.

Let t is time taken by the stone to impact with water surface. Using second equation of motion :

$d=ut+\dfrac{1}{2}gt^2$

u = 0

$d=ut+\dfrac{1}{2}gt^2$

$78.4=\dfrac{1}{2}\times 9.8\times t^2$

t = 4 seconds

Time taken to heard the splash of water, 4.22 - 4 = 0.22 seconds

Let v is the velocity of the sound. It can be calculated using total distance and time taken to heard the splash of water.

$v=\dfrac{d}{t}$

$v=\dfrac{78.4\ m}{0.22\ s}$

v = 356.36 m/s

So, the velocity of sound is 356.36 m/s. Hence, this is the required solution.