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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Subjective Medium Published on 18th 08, 2020
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