Question

A progressive wave is represented by equation y = 5sin(80pi*t - 0.5pi*x) where x and y are in metre and t in second. 

Find (i) Amplitude (ii) Wavelength (iii) Frequency (iv) Time period.

Answer 1

Given,

y = 5 sin(80πt - 0.5πx)

Comparing equation

y = A sin (ωt - kx)

(i) Amplitude A = 5m

(ii) \(k=\frac{2\pi}{λ}\)

\(λ=\frac{2\pi}{k}\)

\(λ=\frac{2\pi0}{0.5}\)

λ = 4 A°

(iii) ω = 2πv

v = \(\frac{ω}{2\pi}\)

v = \(\frac{80\pi}{2\pi}\)

v = 40 Hz

(iv) \(T=\frac{2\pi}{ω}⇒\frac{2\pi}{80\pi}\)

\(⇒ T=\frac{1}{40}sec\)