Question

A 2-meter long wire vibrates with a frequency of 365 Hz when the tension is 500 N. What is the frequency if the tension on the wire is 200 N? [ Answer: frequency = ______ Hz; Round off answer and it must be a whole number]

Answer 1

The fundamental frequency of a vibrating string can be given by

f = (1/2L) where L the length of the string, T the tension and µ the mass per unit length of the wire

When L and µ are constants    f α

Now,   f₁ = 365 Hz    T₁ = 500 N and T₂ = 200 N  

To find f₂

f₂/f₁ =

f₂ = f₁ x    = 365 x = 365 x 0.6325 =230.86 Hz

On rounding to a whole number

f₂ = 231 Hz