A string of mass 2.50 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?
Solution and Explanation
Mass of the string, M = 2.50 kg
Tension in the string, T = 200 N
Length of the string, l = 20.0 m
Mass per unit length, μ \(=\frac{M}{l}=\frac{2.50}{20}=0.125\,kg\,m^{-1}\)
The velocity (v) of the transverse wave in the string is given by the relation:
\(v=\sqrt\frac{T}{μ}\)
\(=\sqrt\frac{200}{0.125}=\sqrt=40\,m/s\)
∴ Time taken by the disturbance to reach the other end, t = \(\frac{l}{v}=\frac{20}{40}=0.50\,s\)
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Concepts Used:
Transverse Waves
Transverse waves are a type of wave in which the disturbance moves perpendicular to the direction of the wave propagation. In other words, the particles of the medium through which the wave is travelling oscillate perpendicular to the direction of the wave's movement.
Examples of transverse waves include light waves, electromagnetic waves, and waves on a string or rope. In these types of waves, the oscillations are perpendicular to the direction of the wave propagation.
Transverse waves have several characteristics that define their behavior. One of these is wavelength, which is the distance between two consecutive crests or troughs in the wave. Another characteristic is frequency, which is the number of waves that pass a given point per unit time. The amplitude of a transverse wave is the maximum displacement of the particles of the medium from their equilibrium position.
Also Read: Amplitude Formula
Transverse waves can be reflected, refracted, and diffracted, just like other types of waves. They obey the laws of superposition, which means that the displacement of the medium caused by two waves passing through each other is equal to the sum of their individual displacements.
Transverse waves have many practical applications, such as in the transmission of information through fiber-optic cables, the creation of images in microscopy, and in the production of electromagnetic radiation for various uses.