Two sinusoidal waves, identical except for phase, travel in the same direction a

Question

Two sinusoidal waves, identical except for phase, travel in the same direction along a string. The phase constant of one is defined to be zero. The waves interfere to produce a resultant wave given by

y(x,t) = A sin (26.0x ? 4.0t + 0.410),

where A = 1.5 mm, x is in meters, and t is in seconds.

I found the wavelength to be 2.42m, correct.

Now i need help with:

1.What is the magnitude of the phase difference between the two waves?

2. What is ther amplitude?

(Steps and units greatly apprecitated, thx)

Explanation / Answer

a)

Phase difference

x=phi

(1/2)x= 0.41 rad

x =0.82 rad

b)

A[sin(pi/2-0.41)+sin(pi/2+0.41)=1.5 mm

2Acos(0.41) =1.5

2Acos(0.41*180/pi)=1.5

2Acos(23.5) =1.5

A =0.8178 mm

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