A stone dropped from the top of a tower of height 300 m 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 and Explanation
Height of the tower, s = 300 m
Initial velocity of the stone, u=0
Acceleration, a = g = 9.8 m/s 2
Speed of sound in air = 340 m/s
The time (t1 ) taken by the stone to strike the water in the pond can be calculated using the second equation of motion, as:
\(s=ut_1+\frac{1}{2}gt_1^2\)
\(300=0+\frac{1}{2}×9.8×t_1^2\)
\(∴ t_1=\sqrt\frac{300×2}{9.8}=7.82\,s\)
Time taken by the sound to reach the top of the tower, \(t_2-\frac{300}{340}=0.88\,s\)
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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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.