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A Stone Dropped from the Top of a Tower of Height 300 M High Splashes into the Water of a Pond Near the Base of the Tower. When is the Splash Heard at the Top Given that the Speed of Sound in Air is 340 M S–1? (G= 9.8 M S–2) - CBSE (Science) Class 11 - Physics

ConceptThe Speed of a Travelling Wave

Question

A stone dropped from the top of a tower of height 300 m high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 340 m s–1? (g= 9.8 m s–2)

Solution 1

Here, h = 300 m, g = 9.8 ms-2  and velocity of sound, v = 340 ms-1 Let t1be the time taken by the stone to reach at the surface of pond.

Then using s = ut + 1/2 at^2 1/2 at^2 => h = 0 xx t + 1/2 "gt"_1^2

:.  t_1 = sqrt((2xx300)/9.8) = 7.82 s

Also if t_2 is the time taken by the sound to reach at a height h, then

t_2 = h/v = 300/340 = 0.88 s

:. Total time after which sound of splash is heard = t_1 + t_2

= 7.82 + 0.88 = 8.7 s

Solution 2

Height of the tower, s = 300 m

Initial velocity of the stone, u = 0

Acceleration, a = g = 9.8 m/s2

Speed of sound in air = 340 m/s

The time (t_1) taken by the stone to strike the water in the pond can be calculated using the second equation of motion, as:

s= ut_1 + 1/2 "gt"_1^2

300 = 0 + 1/2 xx 9.8 xx t_1^2

:. t_1 =sqrt((300xx2)/9.8) = 7.82 s

Time taken by the sound to reach the top of the tower, t_2 = 300/340 = 0.88 s

Therefore, the time after which the splash is heard,t = t_1 + t_2

= 7.82 + 0.88 = 8.7 s

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Solution A Stone Dropped from the Top of a Tower of Height 300 M High Splashes into the Water of a Pond Near the Base of the Tower. When is the Splash Heard at the Top Given that the Speed of Sound in Air is 340 M S–1? (G= 9.8 M S–2) Concept: The Speed of a Travelling Wave.
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