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Standard XII

Physics

Transverse & Longitudinal Waves

A uniform str...

Question

A uniform string is vibrating with a fundamental frequency ' $f$ '. The new frequency, if radius and length both are doubted would be:

2 f

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3 f

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\frac{f}{4}

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\frac{f}{3}

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Solution

The correct option is A $\frac{f}{4}$
Wavelength, $λ = 2 L$
Speed of wave, $v = \sqrt{\frac{T L}{m}}$
$v = f λ$
$⟹ f \propto \frac{1}{\sqrt{m L}}$
$m_{2} = 8 m_{1}$ since volume is increased to 8 times
$L_{2} = 2 L_{1}$
$⟹ f_{2} = f / 4$

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A uniform string is vibrating with a fundamental frequency 'f'. The new frequency, if radius and length both are doubted would be:

The correct option is A f4Wavelength, λ=2LSpeed of wave, v=√TLmv=fλ⟹f∝1√mLm2=8m1 since volume is increased to 8 timesL2=2L1⟹f2=f/4

A uniform string is vibrating with a fundamental frequency ' $f$ '. The new frequency, if radius and length both are doubted would be:

The correct option is A $\frac{f}{4}$
Wavelength, $λ = 2 L$
Speed of wave, $v = \sqrt{\frac{T L}{m}}$
$v = f λ$
$⟹ f \propto \frac{1}{\sqrt{m L}}$
$m_{2} = 8 m_{1}$ since volume is increased to 8 times
$L_{2} = 2 L_{1}$
$⟹ f_{2} = f / 4$