Question

Speed of wave travelling along a stretched string may depend on
a)tension in the string
b)length of the string
Derive the formula for speed of the wave along a stretched string using dimensions?

Answer 1

$$v=T^a\mu^b$$

$$[v]=[T]^a[\mu]^b$$

$$LT^{-1}=(MLT^{-2})^a(ML^{-1})^b$$

$$-1=-2a\to a=\frac{1}{2}$$

$$a=-b\to b=-\frac{1}{2}$$

Thus,

$$v=T^{\frac{1}{2}}\mu^{-\frac{1}{2}}=\sqrt{\frac{T}{\mu}}$$