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Q.

A transverse wave is represented by $2 S i n (w t - k x)$ cm. 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

2

b

$π$

c

$4 π$

d

$2 π$

answer is A.

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Detailed Solution

$y = 2 \sin (w t - K x)$

Maximum particle velocity = $A ω$
Wave velocity = $\frac{ω}{K}$
$\frac{ω}{K} = A ω$

$K = \frac{1}{A} = \frac{2 π}{λ}$

$λ = 2 π A$

$λ = 4 π c m$

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A transverse wave is represented by 2Sinwt−kx cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity will be