Answer to Question #123635 in Mechanics | Relativity for Wilison

Question

The equation y=8Sin(4x–8t) where y is in millimetres,x is in metres and t
is in seconds represent a wave motion.Determine the:
(i) Wavelength
(ii) Frequency
(iii) Period and
(iv) Speed of the wave

Answer 1

GIVEN EQUATION IS;

y = 8Sin(4x–8t)

THE GENERAL FORM OF THE WAVE MOTION IS;

y = asin(kx-wt)

where:

a = amplitude

k = wave number

w = angular frequency

t = time

λ = wavelength

f = frequency

T = period

v = speed

Formula/s;

k = $\frac{2π}{λ}$

w = $2πf$

T = $\frac{1}{f}$

v = $\frac{w}{k}$

substitute all the given;

(i) Wavelength

$λ = \frac{2π}{4m^{-1}}= 1.571m$

(ii) Frequency

$f = \frac{8Hz}{2π} = 1.273Hz$

(iii) Period 

$T = \frac{1}{1.273Hz} = 0.785sec$

(iv) Speed of the wave

$v = \frac{8Hz} {4m^{-1}} = 2m/s$