Obtain the expression for the frequency of transfer vibration in string which depends on tension of the string, length of the string m /l of the string
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Answer:
Let the relation be:
Frequency v = KL
a
f
b
m
c
where k is a dimensionless constant
The dimension of each quantity are:
L=[M
0
L
1
T
o
]
f=[M
1
L
1
T
−2
]
m=[M
1
L
−1
T
0
]
v=[M
0
L
0
T
−1
]
Thus now equating the dimension on both side of the equation:
[M
0
L
0
T−1]=[M
0
L
1
T
0
]
a
[M
1
L
1
T
−2
]
b
[M
1
L
−1
T
0
]
c
thus, b=
2
1
c=−
2
1
a=−1
Thus the formula for frequency is:
V=
L
K
m
f
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