Question

How to check the accuracy of the relation. V is frequency l is the length t is tension m is mass of unit. ...V =1/2l root t/m

Answer 1

In thin string of length L, bound tightly at its two ends, transverse waves can be created.  Let the tension in the string be T and  mass per unit length be m.

   frequency of oscillation (SHM) = f = 1/2L  * √(T/m)

one can use the dimensional analysis:  
 f = [ T⁻¹ ]
L = [ L ]
T = force = [ M L T⁻² ]
m = [ M L⁻¹ ]
so RHS = [ T⁻¹ ] = LHS.
 

Answer 2

The given relation is accurate.

Step-by-step explanation:

The given relation is

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

Where,

v 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 relation 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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