Question #123635

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

is in seconds represent a wave motion.Determine the:

(i) Wavelength

(ii) Frequency

(iii) Period and

(iv) Speed of the wave

Expert's answer

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{2\u03c0}{\u03bb}"

w = "2\u03c0f"

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

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

substitute all the given;

(i) Wavelength

"\u03bb = \\frac{2\u03c0}{4m^{-1}}= 1.571m"

(ii) Frequency

"f = \\frac{8Hz}{2\u03c0} = 1.273Hz"

(iii) Period

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

(iv) Speed of the wave

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

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