First slide

Speed of wave

Question

A long string is lying along X-axis and a tension is maintained in it. Linear mass density is gradually increasing along positive X-axis. A transverse wave is propagating along the string in positive X direction. Then

Easy

A

velocity of propagation is gradually increasing along positive X-direction
B

wavelength is gradually decreasing along positive X-direction.
C

Frequency of wave is gradually decreasing along positive X-direction.
D

wavelength remains unchanged with increasing X.

Solution

velocity of propagation, $V = \sqrt{\frac{T}{μ}}$
As $μ$ is increasing with increase in x, V is decreasing with increase in x. Also since frequency $ν$ remains unchanged during propagation of wave and $λ = \frac{V}{ν}$ , wavelength $λ$ decreases with increase in X.

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