Question

the velocity of waves on a vibrating string depends on the tension in the string and mass per unit length of the string derive an expression for v by using the dimensional analysis method​

Answer 1

Answer:

Here, v∝l

a

T

b

m

c

=kl

a

T

b

m

c

where k is proportionality constant.

Now substituting dimension of each quantities,

[T

−1

]=[L]

a

[MLT

−2

]

b

[M]

c

=[M

b+c

L

a+b

T

−2b

]

Comparing the both sides, b+c=0,a+b=0 and −1=−2b

Thus, b=1/2,c=−b=−1/2,a=−b=−1/2

So, v=k

ml

T

Answer 2

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