- Home
- Standard 11
- Physics
The equation of a wave disturbance is given as : $y = 0.02 cos \left( {\frac{\pi }{2} + 50\pi t} \right) cos (10 x),$ where $x$ and $y$ are in meters and $t$ in seconds. Choose the wrong statement:
Antinode occurs at $x = 0.3 \,\,m$
The wavelength is $ 0.2\,\, m$
The speed of the constituent waves is $4\,\, m/s$
Node occurs at $x = 0.15\,\, m$
Solution
$y=0.02 \cos (\pi / 2+50 \pi \times t) \cos (10 \pi \times x)$
At $x=0.3\,m$
$y=0.02 \cos (\pi / 2+50 \pi \times t) \cos (3 \pi)=-0.02 \cos (\pi / 2+50 \pi \times t)$ (It is
right)
Now compare the given equation by the standard stationary wave equation,
$y=A \cos (\phi+\omega \times t) \cos (2 \pi \lambda \times x)$
$2 \pi \lambda=10 \pi, \lambda=0.2\,m$ (it is also right)
$\text { At } x=0.15\,m$
$y=0.02 \cos (\pi / 2+50 \pi \times t) \cos (\pi / 2)$
and
$v = A \omega=0.02 * 50 \pi=\pi ms ^{-1}$
Hence, option " $C$ " is wrong.
