Question

A plane progressive simple harmonic wave is moving along positive x-direction with speed v = 20 m/s. If amplitude of medium particles is 10 cm and time period of oscillation of medium particle is 2 s, then equation of the plane progressive wave may be (at t = 0, x = 0, y = 5 cm) [x is m and t is in s]

Answer 1

velocity of wave in positive x direction, v = 20m/s

amplitude of wave, A = 10cm = 0.1m

time period of oscillation, T = 2 sec

so, wavelength = velocity of wave/frequency

= velocity of wave × time period

= 20 × 2 = 40m

now, standard equation of plane progressive wave is $y(x,t)=Asin\frac{2\pi}{\lambda}(vt-x+\phi\frac{2\pi}{\lambda})$

$y(x,t)=0.1sin\frac{2\pi}{40}(20t-x+\phi\frac{2\pi}{40})$

at t = 0, x = 0 => y = 5 cm or 0.05m

so, $0.05=0.1sin\frac{\pi}{20}(20.0 - 0+\phi\frac{\pi}{20})$

or, $0.5=sin(\phi)$

or, $\frac{\pi}{6}=\phi$

so, equation of plane progressive wave may be $y(x,t)=0.1sin\left(\pi t-\frac{\pi}{20}x+\frac{\pi}{6}\right)$

Answer 2

Explanation:

here is your answer....it was the first answer which i posting..hope it helps you