Physics

The speed of transverse wave $$v$$ in a stretched string depends on tension $$T$$ in the string and linear mass density (mass per unit length ) $$\mu$$. Find the relation using method  of dimensions.


SOLUTION
Given,

$$Speed=v,Tension=t,Density=\dfrac{m}{L}$$

So, the velocity is given by,

$$KL^AT^BM^C$$

So.$$[M^0LT^{-1}]=[L]^A[MLT^{-2}]^B[\dfrac{M}{L}]^C$$

$$[M^0LT^{-1}]=[M^{B+C}L^{A+B-C}T^{-2B}]$$

On computing the coefficient then we get,

$$B+C=0,A+B-C=1-2B=-1$$

Then we get$$ b=\dfrac{1}{2},c=\dfrac{-1}{2},a=0$$

Thus, $$V=k\sqrt{\dfrac{T}{M}}$$
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