Question

Check the correctness of the equation, Check the correctness of the equation, When the frequency of vibration ‘n’ of a string of length ‘l’ having mass per unit length ‘m’ kept under tension ‘F’ is given by = 1 2 √

Answer 1

The given equation is correct

Step-by-step explanation:

The given equation is

$n=\frac{1}{2l}\sqrt{\frac{F}{m}}$

Where,

n is the frequency

m is mass per unit length

F is force

l is length

If the equation is correct, the dimension on LHS should be equal to the dimensions on RHS

We know that

Dimensions of frequency = [T⁻¹]

Dimensions of length = [L]

Dimensions of Force = [MLT⁻²]

Dimensions of mass per unit length = [ML⁻¹]

Therefore,

Dimensions of LHS in the formula =  [T⁻¹]

Dimensions of RHS in the formula

$=\frac{1}{\text{Dimension of Length}}\sqrt{\frac{\text{Dimension of Force}}{\text{Dimension of Mass per unit Length}}}$

$=\frac{1}{[L]}\sqrt{\frac{[MLT^{-2}]}{[ML^{-1}]}}$

$=\frac{1}{[L]}\sqrt{L^2T^{-2}}$

$=\frac{1}{[L]}\times[LT^{-1}]$

$=[T^{-1}]$

Thus,

Dimensions of LHS = Dimensions of RHS

Therefore, the equation is correct.

Hope this answer is helpful.

Know More:

Q: Assuming that frequency of vibrating string depends upon the load f applied length of the string l and mass per unit length find the relation ?

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