Question
Find the velocity of wave in a string of linear mass density m when stretched to tension T?
Solution
Let velocity of wave in the string vary with ath power of m and bth power of T.
That is,
∴
...(1)
where,
k is constant of proportionality.
If this relation is true then dimensions of each term on both sides will be same.
Substituting the dimension formula of each quantity in equation (1),
Comparing the dimensions of M,L and T on both sides, we get
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On solving we get,
Thus,
That is,
∴
...(1)where,
k is constant of proportionality.
If this relation is true then dimensions of each term on both sides will be same.
Substituting the dimension formula of each quantity in equation (1),
Comparing the dimensions of M,L and T on both sides, we get
and
On solving we get,
Thus,
