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Answers |
| 29. 
( f ) Does the wave travel in the positive or the negative x-direction ? Review class
notes. Remember, a minus sign means rightward (positive) motion, and a positive sign means
leftward.
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| Sp1.
2 waves are described by:
y1(x,t) = 5.0 sin(2.0 x - 10t)
y2(x,t) = 10cos(2.0x - 10t)
Show that the resulting wave y1(x,t) + y2(x,t) =
 .
Find A and the phase constant.
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| sp1. We want to write the sum of the two waves y1
+ y2 in the form:
See eqn. 16.15, page 467.
Thus,
Expand the right hand side of the equation into a sum of sine and cosine:
Thus,
This means that the following two conditions hold: (Please review your trigonometry
book.)
Note:
Solve for A.
Finally, solve for the phase angle. Since the cosine is positive and the sine is negative,
then the phase angle corresponds to the fourth quadrant. Therefore, you can find
the phase angle by first solving for the reference angle and the phase angle in the
following way:
(Review your trigonometry!)
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30.
(a)
Evaluate these at t = 0.20 sec and at x = 1.6 m.
(b)
Evaluate k and from this find the wavelength. Evaluate the angular
frequency omega,
and from this find the frequency f and then the
inverse of f to get the
period. Finally,
Question: What direction does the wave travel, in the positive or negative x
direction ? Remember, a negative sign means positive-x motion and a positive sign means
negative-x motion. |
| 34. 
Use this and the time t = 10 sec to get the distance that the crest travels. For the
direction, see your lecture notes and/or the question in hints to problem 28 (b).
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| Sp2.
A transverse wave traveling on a taut guitar wire has an amplitude of
0.200 mm and a frequency of 500 Hz and travels with speed v = 196
m/s.
(a) Write an equation in SI units of the form
for this wave.
(b) The mass per unit length of this wire is 4.10 g/m. Find the tension
in the wire. |
| Sp2
Hint .
(a)
f = 500 Hz
Find k. A is given.
(b)
Convert the units of the mass per-unit-length to kg/m. Find T=
tension !
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38.
 
Find the frequency f by taking the ratio of the given wave speed to the given
wavelength; From the frequency, find omega. Note: A is given. Compute P.
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