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The velocity v of a wave depends on the tension T in the string,it's length L and mass m derived using dimension the equation of the wave.

The velocity v of a wave depends on the tension T in the string,it's length L and mass m derived using dimension the equation of the wave.

Grade:12th pass

1 Answers

Chirag Sehgal
14 Points
one month ago
Let velocity of wave be v, Tension be T, length be l and mass be m
Given : v ∝ Ta lb mc
v = k Tlm[k is the constant of proportionality]
[LT-1] = [MLT-2]a [L]b [M]c
LT-1 = Ma+c La+b T-2a
Comparing powers of L, M and T individually
a+c = 0 => a=-c
a+b = 1
-2a = -1 => a=1/2
c = – 1/2
b = 1/2
Thus, a = b = 0.5 and c = -0.5
So v = k√(T x l)
                 √m

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