Question

Find the equation of a plane progressive wave travelling along positive: $x-axis$ having amplitude $0.04\,m$, frequency $120 \,Hz$ and speed $360\, m/s$.

• A. $ y=0.04\sin 2\pi (120\,t-x/3) $
• B. $ y=-0.04\sin 2\pi (110\,t-x/3) $
• C. $ y=0.04\sin 2\pi (120\,t+x/3) $
• D. $ y=0.04\sin \,\pi (120\,t-x/3) $

Answer 1

Answer: (A)

The equation of a plane progressive wave moving in the positive direction is given by $y=a \sin (\omega t-k x)$
where, a is amplitude, angular frequency $\omega=2 \pi n, n$, in, $n$ is frequency and propagation constant $k=\frac{2 \pi}{\lambda}, \lambda$ is wavelength.
Here, $a=0.04 m, n=120 Hz \left(s^{-1}\right)$ and wave speed $v =360\,m / s$.
Hence, $\omega=2 \pi n=2 \pi \times 120=240 \pi$ and $v=\frac{\omega}{k}$
or $k=\frac{\omega}{v}=\frac{240 \pi}{360}=\frac{2 \pi}{3}$
Substituting these values of $a, \omega$ and $k$ in the above equation
$y=0.04 \sin \left(240 \pi t-\frac{2 \pi}{3} x\right)$