<p><strong>A transverse wave s represented by y = <math><mrow><mn>2</mn><mi>s</mi><mi>i</mi><mi>n</mi><mrow><mo>(</mo><mrow><mi>ω</mi><mi>t</mi><mo>−</mo><mi>k</mi><mi>x</mi></mrow><mo>)</mo></mrow><mi>c</mi><mi>m</mi><mo>.</mo></mrow></math> The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity. Will be:</strong></p>

Maximum particle velocity = AωWave velocity = ωR⇒ωk=Aω⇒k=1A=12=cmλ=2πk=4πcm

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Physics Class 12th Waves Physics NCERT Exemplar Solutions Class 12th Chapter Fifteen

A transverse wave s represented by y = $2 s i n (ω t - k x) c m .$ The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity. Will be:

Option 1 -

4π

Option 2 -

2π

Option 3 -

Option 4 -

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Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

Maximum particle velocity = $A ω$

Wave velocity = $\frac{ω}{R}$

$\Rightarrow \frac{ω}{k} = A ω$

$\Rightarrow k = \frac{1}{A} = \frac{1}{2} = c m$

$λ = \frac{2 π}{k} = 4 π c m$

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In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning form of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms^-1. The third resonance is observed when the air column has a length of ____________cm.

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According to Concept of resonance tube, we can write

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$\Rightarrow l_{2} = \frac{v}{2 ν} + l_{1} = \frac{336}{400} + 0.20 = 0.84 + 0.20 = 1.04 m = 104 c m$

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Kindly consider the following figure

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alok kumar singh

x = 10 $2 ? (n t ? \frac{x}{?}) c m$

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(n) $λ = 5$

$(n, m)$ : Integers

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$| f_{1} - f_{2} | = \frac{40}{12} = \frac{10}{3}$

$\Rightarrow v (\frac{1}{λ_{1}} - \frac{1}{λ_{2}}) = \frac{10}{3}$

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A transverse wave s represented by y = $2 s i n (ω t - k x) c m .$ The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity. Will be:

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A transverse wave s represented by y = $2 s i n (ω t - k x) c m .$ The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity. Will be: