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Question #f6eef

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Answer 1 · 2018-01-17T16:54:33

$2 m^{- 1}$ $2 m^-1$

Explanation:

Wave number = $\frac{1}{λ}$ $1/lambda$ (where, $λ$ $lambda$ is the wavelength)

From the given equation,comparing it with $y = a sin (ω t - θ)$ $y=a sin (omegat-theta)$ we get, $ω = 100 π$ $omega=100 pi$

so,frequency( $ν$ $nu$ ) = $\frac{ω}{2 π}$ $omega/(2pi)$ = $50 H z$ $50 Hz$

now,we know $c = ν λ$ $c=nulambda$ (where $c$ $c$ is the velocity of the wave)

so, $\frac{1}{λ} = 2 m^{- 1}$ $1/lambda = 2 m^-1$

Answer 2 · 2018-01-17T17:00:06

$k = 3.14 m^{- 1}$ $k=3.14m^-1$

Explanation:

The speed of a wave is:
$v = f λ$ $v=flamda$
In terms of $ω$ $omega$ and wave number:
$v = \frac{2 π f}{2 π \frac{1}{λ}} = \frac{ω}{k}$ $v = (2pif)/(2pi1/lamda) = omega/k$
$rArr k = omega/v = (100pi/cancels)/(100m/cancels) = pi/m = 3.14m^-1$

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