Question

The frequency of v of vibration of stretched string depends on it's length L it's mass per unit length m and the tension T in the string obtain dimensionally an expression for frequency v.

Please it's urgent, and don't answer if you don't know.

Answer 1

ι нσρє υ нєℓρ !!


Here, Bold T denotes tension and T denotes time

[n] = [T]-1

[T] = [MLT-2]

[l] = [L]

[m] = [ML-1]

Now let us assume a relation

n = kT xlymz

=> [ n] = k[T] x[l]y[m]z

=> [T]-1 = k[MLT-2]x[L]y[ML-1]z

=> [T]-1 = k[Mx+z Lx+y-z T-2x]

Comparing the powers on both sides of T

–2x = –1

=> x = ½

Comparing the powers on both sides of L

x + y – z = 0

=> z – y = ½

Comparing the powers on both sides of M

x + z  = 0

=> z = –½

=> y = –1

So our expression becomes

n = kT xlymz

=> n = kT1/2 l-1m-1/2

=> n = (k/l)√(T/m)