Question

Length of a spring is doubled, how will the frequency chnage

Answer 1

Answer:

Explanation:

The velocity of propagation of a wave in a string is proportional to the square rootof the force of tension of the string (T) and inversely proportional to the square root of the linear density (mu) of the string:

v=sqrtT/mu

Because v = frequency f times wavelength lambda, we have

f*lambda = sqrt (T/mu) so f = (sqrt(T/mu) / lambda)

In the conditions given here, lambda doubles and T quadruples, so

f = (sqrt (4*T / mu ) / 2*lambda) = 2* sqrt (T/mu) / (2* lambda)

So f = sqrt(T/mu) / lambda, unchanged from the initial condition