Question

The equation of a progressive wave is given by $y = 5 \,sin(100\pi t -0.4\pi x)$ where $y$ and $x$ are in m and $t$ is in $s$.
(1) The amplitude of the wave is $5\, m$
(2) The wavelength of the wave is $5\, m$
(3) The frequency of the wave is $50\, Hz$
(4) The velocity of the wave is $250\, ms^{-1}$.
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
$y = 5\, sin(100\pi t - 0.4\pi x) \quad ... (i)$
The standard equation of a progressive wave is
$y = a\, sin(\omega t - kx) \quad ... (ii)$
Comparing $(i)$ and $(ii)$, we get
$a= 5\, m$, $\omega = 100\pi\, rad \,s^{-1}$, $k = 0 .4\pi\,m^{-1}$
(1) Amplitude of the wave, $a = 5 \,m$
(2) Wavelength of the wave, $\lambda = \frac{2\pi}{k}= \frac{2\pi}{0.4\pi} = 5\,m$
(3) Frequency of the wave, $\upsilon = \frac{\omega}{2\pi }= \frac{100\pi}{2\pi } = 50\,Hz$
(4) Velocity of the wave, $v = \upsilon\lambda = \left(50\,s^{-1}\right)\left(5\,m\right)$
$= 250\,ms^{-1}$