Two children are at opposite ends of an aluminium rod. One strikes the end of the rod with a stone. Find the ratio of times taken by the sound wave in air and in aluminium to reach the second child.
Approach Solution - 1
Let's consider the length of the aluminum rod as d.
The speed of the sound wave at 25°C in aluminum (VAl) is 6420 m/s.
The time taken for the sound wave to reach the other end of the aluminum rod is given by:
TAl = \(\frac{d}{V_{Al}}\) = \(\frac{d}{6420}\)
The speed of sound in air (Vair) is 346 m/s.
The time taken by sound to reach the other end through air is given by:
Tair = \(\frac{d}{V_{air}}\) = \(\frac{d}{346}\)
Therefore, the ratio of the time taken by sound in aluminum to the time taken in air is:
\(\frac{T_{Al}}{T_{air}}\) = \(\frac{6420}{346}\) = 18.55
Approach Solution -2
The distance between the two children is denoted as d.
Also, let the time it takes for sound to reach the other child through the air be t1 and via aluminium rod be t2.
Velocity of sound in air va = 340 m/s
Therefore, \(t_1=\frac{d}{v_a}=\frac{d}{340}\ \ ....(i)\)
Velocity of sound in aluminium rod vR = 6420 m/s
Therefore, \(t_2=\frac{d}{v_R}=\frac{d}{6420}\ \ .....(ii)\)
Now, by dividing the equation (i) and (ii), we get
\(\frac{t_1}{t_2}=\frac{6420}{340}=18.88\)
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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.