Question

The equation of a progressive wave is given by $y=5sin(100\pi t-0.4\pi x)$ where $y$ and $x$ are in m and $t$ is in $s$.
(1) The amplitude of the wave is $5m$
(2) The wavelength of the wave is $5m$
(3) The frequency of the wave is $50Hz$
(4) The velocity of the wave is $250m{s}^{-1}$.
Which of the following statements are correct?

• A. (1), (2) and (3)
• B. (2) and (3)
• C. (1) and (4)
• D. All are correct

Answer 1

Answer: (D)

The equation of a given progressive wave is
$y=5sin(100\pi t-0.4\pi x)...(i)$
The standard equation of a progressive wave is
$y=asin(\omega t-kx)...(ii)$
Comparing $(i)$ and $(ii)$, we get
$a=5m$, $\omega =100\pi rad{s}^{-1}$, $k=0.4\pi m^{-1}$
(1) Amplitude of the wave, $a=5m$
(2) Wavelength of the wave, $\lambda =\frac{2\pi }{k}=\frac{2\pi }{0.4\pi }=5m$
(3) Frequency of the wave, $\upsilon =\frac{\omega }{2\pi }=\frac{100\pi }{2\pi }=50Hz$
(4) Velocity of the wave, $v=\upsilon \lambda =\left(50s^{-1}\right)\left(5m\right)$
$=250m{s}^{-1}$