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Two waves in one string are described by the wave functions y1= (6 cm)sin (5x- 1.6t)...

Two waves in one string are described by the wave functions y1= (6 cm)sin (5x- 1.6t) and y2 = (6 cm) sin (5x +1.6t+π/2). Find the superposition of waves and name of the resultant wave. Also determine the wave speed, amplitude of the reusltant wave.

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Answer #1

So superposition of this two waves is given by,

y = y1+ y2

So,

y=  (6 cm)sin (5x- 1.6t) + (6 cm)sin(5x+1.6t+π/2)

Or we can write second term as

y=  (6 cm)sin (5x- 1.6t) + (6 cm)cos(5x+1.6t)

So from the formula of

sinx + cosy = 2sin(x+y/2) cos(x-y/2)

So from this we get

y = (12cm) sin(5x+π/4) cos(1.6t-π/4)

So as we can see wave speed is given by,

= Freaquany* wavelength

But the wave represent a standing wave for that case it will not travel in medium so wave velocity should be zero

And Amplitude of wave as you can see

A = 12 cm

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