Question

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

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

Answer 1

Answer: (D)

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