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Speed Of Transverse Wave On A String MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

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  • Speed of transverse wave on a string is considered one of the most asked concept.

  • 38 Questions around this concept.

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When temperature increases, the frequency of a tuning fork

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Speed of transverse wave on a string

The distance between two successive crests is 1 wavelength, λ. Thus in one time period, the wave will travel 1 wavelength in distance. Thus the speed of the wave, v is:

v=\frac{\lambda }{T}=\frac{\text{Distance travelled }}{\text{time taken}}

The speed of the traverse wave is determined by the restoring force set up in the medium when it is disturbed and the inertial properties ( mass density ) of the medium. The inertial property will in this case be linear mass density \mu .

\mu =\frac{m}{L} where m is the mass of the string and L is length. 

The dimension of   \mu is [ML^{-1}] and T is like force whose dimension is [MLT^{-2}] . we need to combine these dimension to get the dimension of speed v which is[LT^{-1}]

Therefore speed of wave in a string is given as :

v=\sqrt{\frac{T}{\mu }}

Now Let's understand its derivation.

Take a small element of length dl  and mass dm of string as shown in the below figure (a)

Here dl=R(2\theta)

So For figure (b)

\\ \begin{aligned} \frac{dm\times v^{2}}{R} &=2 T \sin \theta \\ & \end{aligned}

For \ small \ \theta \ we \ can \ use \ Sin \theta =\theta \\ \\ \Rightarrow \frac{d m v^{2}}{R} =2 T \theta=T \frac{d l}{R}

V^{2}=\frac{T}{d m / d l} \\

Now using

\mu=\frac{dm}{dl}

we get

\Rightarrow V=\sqrt{\frac{T}{\mu}}

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Speed of transverse wave on a string

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Speed of transverse wave on a string

Physics Part II Textbook for Class XI

Page No. : 374

Line : 11

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