Physics - Sound Wave Question with Solution | TestHub

PhysicsSound WaveStanding waveEasy2 minPYQ_2020

PhysicsEasysingle choice

A uniform wire of length $L$ and diameter $D$ and density $ρ$ is stretched under a tension $T$ . The correct relation between its fundamental frequency $f,$ the length $L$ and the diameter $D$ is

Options:

Answer:

Solution:

Since, we know,

Frequency, $f = \frac{n}{2 L} \sqrt{\frac{T}{m}}$

Where, $T =$ tension in the string,

$L =$ Length of the string

And $m =$ linear mass density of the string.

$∴ m = \frac{M}{L} = \frac{π {(\frac{D}{2})}^{2} \cdot L \cdot ρ}{L} = \frac{π D^{2} ρ}{4}$

Thus, $f = \frac{1}{2 L} \cdot \sqrt{\frac{T}{\frac{π D^{2} ρ}{4}}}$

For fundamental frequency, $n = 1$

$f = \frac{1}{2 L \frac{D}{2}} \sqrt{\frac{T}{π ρ}} = \frac{1}{L D} \cdot \sqrt{\frac{T}{π ρ}}$

$f \propto \frac{1}{L D}$

Stream:JEESubject:PhysicsTopic:Sound WaveSubtopic:Standing wave

⏱ 2mℹ️ Source: PYQ_2020

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