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

wave will be of form A sin(kx-wt)

in y1, y2,y3

k=10 w=2

we know w = 2*pi*f

f = w/2*3.14

frequency = 0.318 hz

we know c=f*lamda

wavelength = 3*10^8/0.318 = 9.4*10^8 mts

wave numbr = w/k

here wave number = 2/10 = 0.2

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wave will be of form A sin(kx-wt)

in y6

k=11 w=2.2

we know w = 2*pi*f

f = w/2*3.14

frequency = 0.35 hz

we know c=f*lamda

wavelength = 3*10^8/0.35 = 8.5*10^8 mts

wave numbr = w/k

here wave number = 2.2/11 = 0.2

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