Question

a wire under tension vibrates with a frequency of 450 hertz what would be the fundamental frequency if the wire were half as long twice as thick and under one-fourth tention:

Answer 1

please verify the answer and let me know !!!

Answer 2

Answer:

159.12 Hz

Explanation:

As per the question,

Given data:

A wire under tension vibrates with a frequency = 450 hertz

According to the speed of the string, we have

$v=\sqrt{\frac{T\cdot l}{m}}$

Let V₁ = 450 Hz

Now,

The wire were half as long twice as thick and under one-fourth tention:

New length = l/4

m = 2m

$V_{1}=\sqrt{\frac{T\cdot l}{m}}$

And

$V_{2}=\sqrt{\frac{T\cdot l}{2m\cdot 4}}$

Divide V₂ by V₁, we get

$\frac{V_{2}}{V_{1}}=\frac{1}{\sqrt{8}}\\V_{2}=\frac{450}{\sqrt{8}}$

∴ v₂ = 159.12 Hz

Hence, the fundamental frequency = 159.12 Hz