Question #184970

A sinusoidal sound wave moves through a medium and is described by the displacement wave function s(x,t)=2.00 cos(15.7x-858t), where is micrometers, x is in meters, and t is in seconds. Calculate the amplitude, wavelength and the speed of the wave.

Expert's answer

when provided with an equation

s(x,t)=2.00 cos(15.7x-858t),

s(x, t) = A cos (k x + ω t)

A= amplitude

so amplitude = "2.0 \\times 10^{-6} \\mu m"

if k= 15.7 then wavelength "\\lambda = \\frac{2\\pi}{k} = \\frac{2\\pi}{15.7}"

"\\lambda= 0.4002 m"

Speed of wave "\\nu= \\frac{\\omega}{k} = \\frac{-858}{15.7}"

"\\nu=" 54.6497 m/s in opposite direction

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