Six different waves are described by the following functions (Distances we in me

Question

Six different waves are described by the following functions (Distances we in meters, times in seconds) y_1 = 5 sin (10x - 2t) y_2 = 5 sin (10x + 2t) y_3 = 5 sin (-10x + 2t) Waves y_1 through y_3 all have the same frequency, wavelength, and wave speed. Calculate their wavelength lambda frequency f wave speed For wave y give its: wavelength lambda frequency f If y_1 and y_4 are superimposed, the result will be { constructive interference, destructive interference, standing waves, beats} If y_3, and y_4 are superimposed, the result will be: {constructive interference, destructive interference standing waves, beats} If y_1 and y_2 are superimposed, the result will be: { constructive interference, destructive interference, standing waves, beats} When waves y, and v, are superimposed, beats will be heard What is the "beat" frequency? (i.e., how many amplitude maxima will be heard per second?)

Explanation / Answer

The general eq for wave is given by,
y = A*sin(kx - w*t)

y1 = 5*sin(10x - 2*t)
k = 10
w = 2

1)
Wavelength , = (2*)/k
= (2*)/10
= 0.628

frequency, f = w/(2*)
f = 2/(2*)
f = 0.318 hz

wave speed, v = f*
v = 0.318 * 0.628
v = 0.199

2)

y1 = 5*sin(11x - 2.2*t)
k = 11
w = 2.2

Wavelength , = (2*)/k
= (2*)/11
= 0.571

frequency, f = w/(2*)
f = 2.2/(2*)
f = 0.350 hz

wave speed, v =  f*
v = 0.350 * 0.571
v = 0.199

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