3. Two harmonic waves traveling in a string are described by the following wave

Question

3. Two harmonic waves traveling in a string are described by the following wave functions Y1 = 4sin ((Pi / 2)(x - 1.2 t)] cm and Y2 = 4 sin (Pi/2)( (x +1.2 t)3 cm, where x is in cm and t in s. (a) Use the trigonometric identity . sin(alpha + or - B)=sin alpha cos Beta +/- cos alpha sin Beta to write the wave function for the resultant wave in the string, (b) Determine the amplitude, wavelength, and period of the resultant wave. (C) Calculate the maximum transverse displacement of the string It the point x = 0.75 cm.

Explanation / Answer

Y = y1 + y2

y1 = Asin (alfa + beta) = A*(sinalfa*cos beta + cos alfa*sinbeta)

y2 = Asin ( alf - beta) = A*(sinalfa*cos beta - cos alfa*sinbeta)

Y = y1 + y2

Y = 2*A*sinalfa*cos beta

here alfa = pix/2

beta = pi*1.2*t/2

Y = 2*4*sin[pix/2] * cos[ pi*1.2t/2) ]

Y = 8* sin(pi*x/2) *cos(0.6*pi*t)

b) amplitude = 8* sin(pi*x/2)

c) y = 8*sin(pi*0.75/2)

y = 7.38 cm

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