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 GHz.

(4) The velocity of the wave is 250 m 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)

All are correct

Answer 2

The equations of a given progressive wave is

y = 5 sin $(100\pi t - 0.4\pi x)$ ….. (i)

The standard equations of a progressive wave is

$y = a\sin{}(\omega t - kx)$ ….. (ii)

Comparing (i) and (ii), we get

$a = 5m,\omega = 100\pi rads^{- 1},k = 0.4\pi m^{- 1}$

(1) Amplitude of the wave, a = 5 m

(2) Wavelength of the wave,

$\lambda = \frac{2\pi}{k} = \frac{2\pi}{0.4\pi} = 5m$

(3) Frequency of the wave,

$\upsilon = \frac{\omega}{2\pi} = \frac{100\pi}{2\pi} = 50Hz$

(4) Velocity of the wave,

$v = \upsilon\lambda = (50s^{- 1})(5m)$

$= 250ms^{- 1}$