Question

Two waves are described by
y₁ = 0.29 sin[π(7x - 110t)]
and
y₂ = 0.29 sin[π(7x - 110t) + π/8],
where y₁, y₂, and x are in meters and t is in seconds. When these two waves are combined, a traveling wave is produced. What are the (a)amplitude, (b) wave speed, and (c) wavelength of that traveling wave?

Answer 1

the resultant wave equation is,

y = y1+y2

= [0.29 sin[π(7x - 110t)]]+[0.29 sin[π(7x - 110t) + π/8]]

= 0.29{sin + sin[-π/8]

here, = π(7x - 110t). thus, the amplitude is,

A = 2Acos[] = 2*0.29*cos(π/16) = 0.568 m

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the frequency is calculated as follows:

f = w/2*pi = 110*pi/2*pi = 55 Hz

the wavelength is,

lambda = 2*pi/k = 2*pi/7*pi = 0.2857 m

the wave speed is,

v = f*lambda = 55*0.2857 = 15.7 m/s