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Speed of transverse wave on a string is considered one of the most asked concept.
38 Questions around this concept.
When temperature increases, the frequency of a tuning fork
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:
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 .
where m is the mass of the string and L is length.
The dimension of is and T is like force whose dimension is . we need to combine these dimension to get the dimension of speed v which is.
Therefore speed of wave in a string is given as :
Now Let's understand its derivation.
Take a small element of length and mass dm of string as shown in the below figure (a)
Here
So For figure (b)
Now using
we get
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