# Maximum Transverse Speed

As we know that the wave motion are of two types: One is called the transverse wave motion and the other is called the longitudinal wave motion. A transverse wave motion is that wave motion in which individual particles of the medium execute simple harmonic motion about their mean position in the direction perpendicular to the direction of propagation of wave motion.

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The transverse wave travels in a medium in the form of the crests and troughs. The speed of the transverse wave is different in different mediums and in different modes. Let us discuss about the maximum transverse speed.Image based on Transverse wave speed mechanismImage based on Transverse wave speed mechanismMaximum Speed of Transverse Wave

The speed of transverse wave in case of the stretched string is given by`V = (T/m)^(1/2) `Where, T be the tension in the string and m be the mass of the string per unit length or we can say that m be the linear density (mass per unit length) of the string. It is remembered that the velocity of the transverse wave propagating along a string depends only on the characteristics of the string (that means the value of T and m).

It does not depend upon the frequency of the wave. The velocity of the transverse waves in a solid is given by` V="(eta/rho)^(1/2)`"Where, `eta` is the modulus of rigidity of the solid material and `rho` be the density of the solid material. The speed of the transverse wave is maximum when it travels in vacuum. The maximum speed of the transverse wave is 3 ´108 metre per second.Example Based on the Maximum Speed of Transverse WaveCalculate the speed of the transverse waves in a copper wire of 1 square mm area of cross section under the tension produced by 1 kg wt.

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The relative density of copper is 8.93.Solution:Here, a = 1 mm2 = 10-2 m2, r = 8.93 g/cc, T = 1 kg wt = 9.8 Newton = 9.8 ´105 dyneMass of unit length of wireM = a *1 * r = 10-2 * 8.93 g per cm`V = (T/m)^(1/2) `V = [(9.8 *105) / (8.93 *10-2)] 1/2V = 3.312 *103 cm / s = 33.12 m / s