The ends of a stretched wire of length l are fixed at x = 0 and x = l . In one experiment, the displacement of the wire is y 1 = a sin ⁡ π x l sin ⁡ ω t and energy E 1 and in another experiment, its displacement is y 2 = a sin ⁡ 3 π x l sin ⁡ 3 ω t and energy is E 2 then

In first case freq. ⇒ ω 1 = ω In second case freq. ω 2 = 3 ω ∵ E n e r g y α f r e q . 2 E 1 E 2 = ω 2 ( 3 ω ) 2 ⇒ E 2 = 9 E 1

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Physics - Sound Wave Question with Solution | TestHub

PhysicsSound WaveStanding waveHard2 minPYQ_2020

PhysicsHardsingle choice

The ends of a stretched wire of length $l$ are fixed at $x = 0$ and $x = l$ . In one experiment, the displacement of the wire is $y_{1} = a \sin (\frac{π x}{l}) (\sin ω t)$ and energy $E_{1}$ and in another experiment, its displacement is $y_{2} = a \sin (\frac{3 π x}{l}) (\sin 3 ω t)$ and energy is $E_{2}$ then

Options:

Answer:

Solution:

In first case freq. $\Rightarrow ω_{1} = ω$

In second case freq. $ω_{2} = 3 ω$

$∵ E n e r g y α {(f r e q .)}^{2}$

$\frac{E_{1}}{E_{2}} = \frac{ω^{2}}{(3 ω)^{2}}$

$\Rightarrow E_{2} = 9 E_{1}$

Stream:JEESubject:PhysicsTopic:Sound WaveSubtopic:Standing wave

⏱ 2mℹ️ Source: PYQ_2020

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