Question

# These two waves travel along the same string: y1 = (4.14 mm) sin(2.31πx - 430πt) y2...

These two waves travel along the same string:

 y1 = (4.14 mm) sin(2.31πx - 430πt) y2 = (5.79 mm) sin(2.31πx - 430πt + 0.771πrad).

What are (a) the amplitude and (b) the phase angle (relative to wave 1) of the resultant wave? (c) If a third wave of amplitude 5.24 mm is also to be sent along the string in the same direction as the first two waves, what should be its phase angle in order to maximize the amplitude of the new resultant wave?

#### Homework Answers

Answer #1

y = y1 + y2

y = 4.14 sin(2.31πx - 430πt) + (5.79 mm) sin(2.31πx - 430πt + 0.771πrad)

y = 4.14*sin(2.31πx - 430πt) + (5.79 mm) sin(2.31πx - 430πt )*cos0.771π + (5.79 mm) cos(2.31πx - 430πt )*sin0.771π

y = sin(2.31πx - 430πt)*[4.14 + (5.79 *cos0.771π) ] + cos(2.31πx - 430πt )* (5.79*sin0.771π )

R*costheta = 4.14 + (5.79 *cos0.771π)

R*sintheta = (5.79*sin0.771π )

y12 = R*sin(2.31πx - 430πt+theta)

R = sqrt(4.14^2+5.79^2+(2*4.14*5.79*cos(0.771pi))

R = 3.821 mm

+++++++++++++++++++++++++

phase angle = tan^-1((5.79*sin0.771π )/(4.14 + (5.79 *cos0.771π)))

phase angle = -1.514 rad

Know the answer?
Your Answer:

#### Post as a guest

Your Name:

What's your source?

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Not the answer you're looking for?
Ask your own homework help question
ADVERTISEMENT
##### Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

ADVERTISEMENT