Question

keeping material of wire and tension fixed how will the resonant length change if the diameter of the wire is increased ​

Answer 1

Answer:

for constant value of frequency if we increase the diameter of wire then we need to decrease the length by same factor.

Explanation:

As we know that resonant length is L then let say for Nth resonant condition we will have

$N\frac{\lambda}{2} = L$

so we have

$\lambda = \frac{2L}{N}$

now velocity of the wave in the string is given as

$v = \sqrt{\frac{T}{\rho \pi r^2}}$

now for resonant frequency we have

$f = \frac{v}{\lambda}$

$f = \frac{N}{2L}\sqrt{\frac{T}{\rho \pi r^2}}$

so here we can say that for constant value of frequency if we increase the diameter of wire then we need to decrease the length by same factor.

#Learn

Topic : Resonance Frequency in wire

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