A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 20 °C = 343 m s–1 .
Solution and Explanation
Length of the steel wire, l = 12 m
Mass of the steel wire, m = 2.10 kg
Velocity of the transverse wave, v = 343 m/s
Mass per unit length, \(μ=\frac{m}{l}=\frac{2.10}{12}=0.175\,kg,m^{-1}\)
For tension T, velocity of the transverse wave can be obtained using the relation:
\(v=\sqrt\frac{T}{μ}\)
\(\therefore\,T=v^2μ\)
= (343)2 × 0.175 = 20588.575≈ 2.06 × 104 N
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Top CBSE Class XI Transverse and longitudinal waves Questions
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A transverse harmonic wave on a string is described by
y(x, t) = 3.0 sin (36 t + 0.018 x + \(\frac{π}{4}\))
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For the travelling harmonic wave
y(x, t) = 2.0 cos 2π (10t – 0.0080 x + 0.35)
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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.