CBSE Class 11-science Answered
The frequency of stretched string depends upon length of string (l), tension in the string (t), and m per unit length (u) of the string. find the expression of vibration of string using method of dimension
Asked by tejpaljeet4 | 03 Mar, 2021, 12:13: PM
Expert Answer
Let frequency of vibration be ν , dimension of frequency of vibration = [ Mo Lo T-1 ]
Let length of string be l , dimension of l = [ Mo L To ]
Let Tension be T , dimension of Tension ( force ) = [ M L T-2 ]
Let mass per unit length be m , dimension of m = [ M L-1 ]
Let frequency of vibration ν = lx Ty mz ..................... (1)
where x , y and z are to be determined from dimension analysis
If we apply dimensions on both side of eqn.(1), we get
[ Mo Lo T-1 ] = [ Mo L To ]x [ M L T -2 ]y [ M L-1 ]z
By applying law of indices to the above expression we gte
y+z = 0
x +y-z = 0
-2y = -1
y = 1/2 , z = -1/2 , x = -1
Frequency of vibration ν is given as
where k is numerical constant without any dimension
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