Question

A transverse harmonic wave on a string is described
by $y(x,t)=3$sin $(36t+0.08x+\frac{\pi }{4})$ where $x$ and
$y$ are in cm and $t$ is in $s$. Which of the following statement incorrect?

• A. The wave is travelling in negative $x-$direction.
• B. The amplitude of the wave is $3$ cm.
• C. The speed of the wave is $20m{s}^{-1}$.
• D. The frequency of the wave is $\frac{9}{\pi }$ Hz.

Answer 1

Answer: (D)

The frequency of the wave is $\frac{9}{\pi }$ Hz.

The given transverse harmonic wave equation is
$y=3$sin $(36t+0.018x+\frac{\pi }{4})$ ....(i)
As there is positive sign between $t$ and $x$ terms therefore the given wave is travelling in the negative $x$ direction.
The standard transverse harmonic wave equation is
$y=a$sin$(\omega t+kx+\varphi )$ ....(ii)
Comparing (i) and (ii), we get
$a=3$cm, $\omega =36$ rad $s^{-1},k=0.018$ rad $c{m}^{-1}$
$\therefore$ Amplitude of wave, $a=3$cm

Frequency of the wave, $\upsilon =\frac{\omega }{2\pi }=\frac{36}{2\pi }=\frac{18}{\pi }$Hz

Velocity $V=\frac{\omega }{k}=\frac{36rad{s}^{-1}}{0.018radc{m}^{-1}}=2000cm{s}^{-1}=20m{s}^{-1}$