The friquency of vibration of a string depends on the length L between the nodes,the tension F in the string and its mass per unit length m.Guess the expression for its friquency from dimensional analysis.

Question

anonymous · Answer

some one there help in this please

anonymous · Answer

Oh dear, why would we use dimensional analysis when we could solve exactly? Oh well, first we assume frequncy f is a function of L, T, and M with maybe a constant involved. Then,

$$f=KL^aT^bM^c$$ 
The square brackets show we are going to look at units, K is scalar. L has units length (l), T has units force (N), and M has units mass (m). Frequency is is Hz or one over t.

$$[Hz]=[\frac{1}{t}]=K[l]^a[N]^b[m]=K[l]^a[\frac{m l}{t^2}]^b[m]^c$$ We choose a, b ,c to make this work.

Take: 
$$a=-1/2;b=-1/2;c=1/2$$ Check this now,

$$[l]^{-1/2}[ml/t^2]^{1/2}[m]^{-1/2}=[1/t]\implies f=K(\frac{T}{LM})^{1/2}$$