A stone is dropped from the top of a tower 500 m high into a pond of water at the base of the tower. When is the splash heard at the top?
Given, g = 10 ms–2 and speed of sound = 340 ms–1.
Given, g = 10 ms–2 and speed of sound = 340 ms–1.
Solution and Explanation
Tower Height (s): 500 m
Sound Velocity (v): 340 m/s
Gravity Acceleration (g): 10 m/s²
Stone's Initial Velocity (u): 0
Time (t1) taken by the stone to fall to the tower base:
Applying the second equation of motion,
\(s=ut_1+\frac{1}{2}g(t_1)^2\)
500=0⋅t1+\(\frac{1}{2}\)⋅10⋅(t1)2
(t1)2=100
t1=10s
Time (t2) taken by sound to reach the top from the tower base:
t2 = \(\frac{s}{v}\) = \(\frac{500}{340}\) \(≈\) 1.47s
Total time (t) is the sum of t1 and t2:
t1+t2=10+1.47=11.47s
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Concepts Used:
Sound
Sound is a vibration that propagates the mechanical wave of displacement and pressure, through a medium can be of any matter. In other words, the sound is the thin line between Music sound and Noise.
Types of Sounds:
Sound can be divided into two types depending on its frequency. The following are:-
Infrasonic Waves:
- Infrasonic waves have a frequency lower than 20 Hz. Since it is below the human hearing range, it is inaudible to humans.
- However, several other living organisms use these waves to communicate, whales, sharks, elephants, hippopotamus, etc. these waves are also used in the scientific field, it is used to study upcoming earthquakes, volcanic eruptions, human heart rates, rock formation stages, etc.
Ultrasonic waves:
- Ultrasonic waves have a frequency higher than 20 kHz. Since it is above the human hearing range, it is inaudible to humans.
- These waves are used in the scientific field, it is used to study human heart rates, to take sonograms, navigation of directions, imaging things, uniform sample mixing, communication, testing of samples, etc.