Question

e
5.
Using dimensional analysis obtain an
expression for the speed of transverse
waves in a stretched string.
​

Answer 1

Answer:

Dimensional Analysis to show how the speed is related to mass per unit length and Tension

• μ = [M]/[L] = [ML-1] (i)

• T=F=ma =[M][LT-2] = [MLT-2] (ii)

• Dividing equation (i) by (ii) :- [ML-1]/[MLT-2] = L-2T-2 =[T/L]2 =[TL-1]2 =1/v2

• Therefore μ/T = 1/v2

• v=C√T/ μ where C=dimensionless constant.