Question

A string of linear density 1.5 g/m is under a tension of 20 N. What should be its length if its fundamental resonance frequency is 220 Hz

Answer 1

Answer:

L= 0.262 m

Explanation:

Given that

Linear velocity ,μ = 1.5 g/m

μ = 1.5 x 10⁻³ Kg/m

Tension ,T= 20 N

Fundamental Frequency ,f= 220 Hz

We know that fundamental frequency given as

$f=\dfrac{1}{2L}\times\sqrt{ \dfrac{T}{\mu}}$

L=length

Now by putting the values

$L=\dfrac{1}{2f}\times\sqrt{ \dfrac{T}{\mu}}$

$L=\dfrac{1}{2\times 220}\times\sqrt{ \dfrac{20}{1.5\times 10^{-3}}}$

L= 0.262 m

Therefore the length will be 0.262 m.