Question

The equation of a stationary wave is given by $ y= 0.5 sin (\frac{2\pi}{3}x) cos (120 \pi t)$ where $x, y $ are in $m$ and $t$ in $s$.
Which of the following statements is wrong?

• A. The frequency of the wave is $60\, Hz$
• B. The speed of the wave is $180 \,\,ms^{-1}$
• C. The wavelength of the wave is $3 \,m$
• D. The speed of the wave is $90\, m\, s^{-1}$

Answer 1

Answer: (D)

The given equation of a stationary wave is
$y = 0.5 \,sin \left(\frac{2\pi}{3} x\right)cos \left(120 \pi t\right)\quad...\left(i\right)$
The standard equation of a stationary wave is
$y = 2 asin\left(kx\right)cos\left(\omega t\right) \quad...\left(ii\right) $
Comparing $\left(i\right)$ and $\left(ii\right)$ we get,
$k =\frac{2\pi}{3} or \frac{2\pi}{\lambda} = \frac{2\pi}{3}$ or $\lambda = 3\, m$
$ \omega = 120 \pi$ or $2\pi\upsilon = 120\pi$ or $\upsilon = 60 \,Hz $
Speed of the wave, $\upsilon = \upsilon\lambda = 180 \,m\, s^{-1} $