# Question #f6eef

Jan 17, 2018

$2 {m}^{-} 1$

#### Explanation:

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

From the given equation,comparing it with $y = a \sin \left(\omega t - \theta\right)$ we get, $\omega = 100 \pi$

so,frequency($\nu$) =$\frac{\omega}{2 \pi}$ = $50 H z$

now,we know $c = \nu \lambda$ (where $c$ is the velocity of the wave)

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

Jan 17, 2018

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

#### Explanation:

The speed of a wave is:
$v = f l a m \mathrm{da}$
In terms of $\omega$ and wave number:
$v = \frac{2 \pi f}{2 \pi \frac{1}{l} a m \mathrm{da}} = \frac{\omega}{k}$
$\Rightarrow k = \frac{\omega}{v} = \frac{100 \frac{\pi}{\cancel{s}}}{100 \frac{m}{\cancel{s}}} = \frac{\pi}{m} = 3.14 {m}^{-} 1$