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 - π

Option 4 - 2

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Answered by

Alok Kumar Singh | Contributor-Level 10

6 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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A longitudinal wave is represented by x = 10 sin 2p $(n t - \frac{x}{λ}) c m .$  The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:

Alok Kumar Singh

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(n) $λ = 5$

$(n, m)$ : Integers

$\begin{array}{r} (\frac{2 m + 1}{2}) λ = \frac{3}{2} \\ \Rightarrow \frac{3 / 2}{5} = \frac{2 m + 1}{2 n} \\ \Rightarrow 3 n = 10 m + 5 \end{array}$

$N, m$ are integers.

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$\begin{array}{l} m = 4 & n = 15 & λ = \frac{1}{3} \\ m = 7 & n = 25 & λ = \frac{1}{5} \end{array}$

The velocity of sound in a gas, in which two wavelengths 4.08m and 4.16m produce 40 beats in 12s, will be

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

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

$\Rightarrow$ $V$ $=$ $\frac{10}{3}$ $\times$ $\frac{λ_{1} λ_{2}}{λ_{2} - λ_{1}}$ $=$ $\frac{10}{3}$ $\times$ $\frac{4.08 \times 4.16}{. 08}$ $=$ $\frac{10}{3}$ $\times$ $\frac{408 \times 4.16}{8}$ $=$ $7$ $0$ $7$ $.$ $2$ $m$ $/$

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A transverse wave s represented by y = 2sin(ωt−kx)cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity. Will be: