The equation of the progressive wave is y = 12 cos(40t - 4x)
The general wave equation is given by:
y = A sin(ωt - kx)
Where A is the amplitude, ω is the angular frequency = 2πf, f is the frequency, k is the wave number and y, x is the displacement.
Given the equation for a progressive wave is y=6 cos(20t-4x). Hence:
The amplitude A = 6,
ω = 20 = 2πf
f = 20/2π = 3.183 Hz
Twice the amplitude = 2 * 6 = 12, twice the frequency = 2 * 3.183.
ω = 2π(3.183*2) = 40
Therefore the other progressive wave has an equation of:
y = 12 cos(40t - 4x)
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