Download Set #12 - McMaster Physics and Astronomy

Practice Problems 12
1. Two identical sinusoidal waves with wavelengths of 2.65 m travel in the same
direction at a speed of 1.30 m/s. The second wave originates from the same point as the
first, but at a later time. Determine the minimum possible time interval between the
starting moments of the two waves if the amplitude of the resultant wave is the same as
that of each of the two initial waves.
Answer: 6.79e-01 s
2. A 0.0115 kg, 1.87 m long wire is fixed at both ends and vibrates in its simplest mode
under a tension of 208 N. When a tuning fork is placed near the wire, a beat frequency of
5.00 Hz is heard. What are the possible frequencies of the tuning fork? (enter the smaller
frequency first)
Answer: 4.42E+01 Hz 5.42E+01 Hz
3. Two loudspeakers are placed on a wall 2.11 m apart. A listener stands 2.95 m from the
wall directly in front of one of the speakers. The speakers are being driven by a single
oscillator at a frequency of 292 Hz. What is the phase difference between the two waves
then they reach the observer? Take the speed of sound as 343 m/s.
Answer: 3.62e+00 rad
4. What is the frequency closest to 292 Hz to which the oscillator may be adjusted such
that the observer hears minimal sound?
Answer: 2.53e+02 Hz
5. Two speakers are driven by the same oscillator with frequency of 169 Hz. They are
located 3.63 m apart on a vertical pole. A man really far away walks straight toward the
lower speaker in a direction perpendicular to the pole, as shown in the figure.
How far is he from the pole at the first moment he hears a minimum in sound intensity
(short of infinity) if the speed on sound is 330 m/s?
Answer: 6.26e+00 m
6. Light of wavelength 699.0 nm illuminates a double slit, and the interference pattern is
observed on a screen. At the position of the m=2.00 bright fringe, how much farther is it
to the more distant slit than to the nearer slit?
Answer: 1.40e+03 nm
7 Light from a sodium lamp of wavelength 517.0 nm illuminates two narrow slits. The
fringe spacing on a screen 143.3 cm behind the slits is 4.41 mm. What is the spacing
between the two slits?
Answer: 1.68e-04 m
8. In a double-slit experiment the slit separation is 264.0 times the wavelenth of the light.
What is the angular separation between the two adjacent fringes?
Answer: 2.17e-01 deg
9. Waves from a radio station have a wavelength of 294 m. They travel by two paths to a
home receiver 14.8 km from the transmitter. One path is a direct path, and the other is by
reflection from a mountain directly behind the home receiver. What is the minimum
distance from the mountain to the receiver that produces destructive interference at the
receiver? (Assume that no phase change occurs on reflection from the mountain.)
Answer: 7.35e+01 m
10. Radio waves from a star, of wavelength 252 m, reach a radio telescope by two
separate paths. One is a direct path to the receiver, which is situated on the edge of a cliff
by the ocean. The second is by reflection off the water. The first minimum of destructive
interference occurs when the star is 22.7° above the horizon. Calculate the height of the
cliff. (Assume no phase change on reflection.)
Answer: 1.63e+02 m
11. In a location where the speed of sound is 339 m/s, a 1966 Hz sound wave impinges
on two slits 27.0 cm apart. At what angle is the first-order maximum located?
Answer: 3.97e+01 deg
12. If the sound wave is replaced by 3.31 cm microwaves, what slit separation gives the
same angle for the first-order maximum?
Answer: 5.18e-02 m
13. If the slit separation is 1.61 µm, what frequency of light gives the same first
maximum angle?
Answer: 2.92e+14 Hz
14. The intensity on the screen at a certain point in a double-slit interference pattern is
66.8% of the maximum value. What minimum phase difference (in radians) between
sources produces this result?
Answer: 1.23e+00 rad
15. Express the phase difference as a path difference for 419 nm light.
Answer: 8.19e-08 m
16. In a Young's interference experiment, the two slits are separated by 0.155 mm, and
the incident light includes light of wavelengths λ1 = 540 nm and λ2 = 450 nm. The
overlapping interference patterns are formed on a screen 1.27 m from the slits. Calculate
the minimum distance from the center of the screen to the point where a bright line of the
λ1 light coincides with a bright line of the λ2 light.
Answer: 2.21E+00 cm