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CBSE Class 11-science Answered

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

Asked by jullypradhan001 | 05 Aug, 2018, 11:48: PM
Expert Answer
Frequency is denoted by 'n' 
 
let us consider 
 
 n= klxTymz ...(1)
 
Writing dimension for each quantity,
n → [M0L0-1]
l→ [M0L1T0]
T→[M1L1T-2]
m→[M1L-1T0]
 
Substituting dimensions in equation (1),
[M0L0T-1] = k[M0L1T0]x [M1L1T-2]y [M1L-1T0]z
 
[M0L0T-1] = k [My+z Lx+y-z T-2y] ...(2)
 
From (2),
y+z = 0
x+y-z =0
-2y = -1  ....(3)
 
Solving equations (3) simultanously we get,
 
x = -1, y = 1/2 and z = -1/2
 
Substituting these value of x,y and z in equation (1),

 n= kl-1T1/2m-1/2
 
rightwards double arrow space n equals space k over l square root of T over m end root
This is the formula for frequency of vibration for stretched string. 
 
 
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