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The frequency of vibration of string dep...

The frequency of vibration of 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 frequency from dimensional analysis.

Text Solution

Verified by Experts

The correct Answer is:
`(k)/(L)sqrt((F)/(m))`
Frequency `prop L^(a)F^(b) (m)^(c)=L^(a)F^(b)((M)/(L))^(c)`
`(1)/(T)=kL^(a)(MLT^(-2))^(b)((M)/(L))^(c) " " [krarr"Proporsionality constant"]`
`T^(-1)=kL^(a+b-c)M^(b+c)T^(-2c)`
On comparing `c=-(1)/(2), b=+(1)/(2 ),a=1`
frequency `(k)/(L)sqrt((F)/(m))`
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