Question

A transverse harmonic wave on a string is described by $y\left(x,t\right)=3sin\left(36t+0.018x+\frac{\pi }{4}\right)$ where $x$ and $y$ are in $cm$ and $t$ is in $s$. Which of the following statements is incorrect?

• A. The wave is travelling in negative $x$-direction
• B. The amplitude of the wave is $3cm$
• 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 given transverse harmonic wave equation is
$y=3sin\left(36t+0.018x+\frac{\pi }{4}\right)\dots \left(i\right)$
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
$y=asin\left(\omega t+kx+\varphi \right)\dots \left(ii\right)$
Comparing $\left(i\right)$ and $\left(ii\right)$, we get
$a=3cm$, $\omega =36rad{s}^{-1},k=0.018radc{m}^{-1}$
$\therefore$ Amplitude of wave, $a=3cm$
Frequency of the wave, $\upsilon =\frac{\omega }{2\pi }=\frac{36}{2\pi }=\frac{18}{\pi }Hz$
Velocity of the wave
$v=\frac{\omega }{k}=\frac{36rad{s}^{-1}}{0.018radc{m}^{-1}}$
$=2000cm{s}^{-1}=20m{s}^{-1}$