Waves
1. Two pulses of equal width and height are traveling in opposite directions on the same string
as shown.
When the pulses completely overlap, what is the shape of the string?
2. Red light of wavelength 6.8x10-7 m enters glass with an index of refraction of 1.583 from
air, with an angle of incidence of 38o. Calculate:
a. The angle of refraction
b. The speed of light in the glass
c. The wavelength of the light in the glass
3. A ray of light is incident on a rectangular block of glass of index of refraction 1.450 at an
angle of 40o, as shown.
If the thickness of the block is 4.00 cm, calculate the amount d by which the ray is deviated.
4. A radio station, R, emits radio waves of wavelength 1600 m which reach a house, H,
directly and after reflection from a mountain, M, behind the house as shown.
If the reception at the house is very poor, what is the shortest possible distance between the
house and mountain?
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5. A car moves along a road that joins the twin antennas of a radio station that is broadcasting
at a frequency of 90.0 MHz as shown.
When in position A, the reception is good but it drops to almost zero at position B. What is
the minimum distance AB?
6. A single slit of width 1.50 μm is illuminated with light of wavelength 500.0 nm. Calculate
the angular width of the central maximum.
7. Microwaves of wavelength 2.80 cm fall on a slit and the central maximum at a distance of
1.0 m from the slit is found to have a half width (i.e. distance from middle of central
maximum to the first minimum) of 0.67 m. Calculate the width of the slit.
8. Could a telescope with an objective lens of diameter 20 cm resolve two objects a distance
of 10 km away separated by 1 cm? (Assume we are using a wavelength of 600 nm).
9. The headlights of a car are separated by a distance of 1.4 m. At what distance would these
be resolved as two separate sources by a lens of diameter 5 cm if a wavelength of 500 nm is
being used?
10. A source approaches a stationary observer at 40 ms-1 emitting sound of frequency 500 Hz.
What frequency does the observer measure? The speed of sound is 343 ms-1.
11. A source is moving away from a stationary observer at 32 ms-1 emitting sound of frequency
480 Hz. What frequency does the observer measure? The speed of sound is 343 ms-1.
12. A sound wave of frequency 512 Hz is emitted by a stationary source toward an observer
who is moving away at 12 ms-1. What frequency does the observer measure? The speed of
sound is 343 ms-1.
13. A sound wave of frequency 628 Hz is emitted by a stationary source toward an observer
who is approaching at 25 ms-1. What frequency does the observer measure? The speed of
sound is 343 ms-1.
14. A sound wave of frequency 500 Hz is emitted by a moving source toward a stationary
observer. The signal is reflected by the observer and received by the source, where the
frequency is measured to be 512 Hz. What is the speed of the source? The speed of sound
is 343 ms-1.
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15. A source emits waves of frequency f towards an object moving away from the source. The
waves are reflected by the object and are received back at the source. The speed of the
object is v and the speed of the waves is c.
a. Deduce that the frequency of the reflected waves as measured by an observer at the
source is given by
1 − vc
f '= f
1 + vc
b. If vc is small, it can be shown mathematically that
1
v
≈1−
v
1+ c
c
Deduce that the magnitude of the frequency shift measured by the observer at the
source becomes
2v
∆f =
f
c
16. A glass tube is closed at one end. The air column it contains has a length that can be varied
between 0.50m and 1.50 m. If a tuning fork of frequency 306 Hz is sounded at the top of
the tube, at which lengths of the air column would resonance occur? (Take the speed of
sound to be 330 ms-1.)
17. A tube with both ends open has two consecutive harmonics of frequency 300 Hz and 360
Hz.
a. What is the length of the tube?
b. What are the harmonics?
(Take the speed of sound to be 330 ms-1.)
18. A string with both ends fixed vibrates in the third harmonic mode. The length of the string
is 6.0 m and the speed of the wave is 120 ms-1. Calculate the wavelength of the wave on
the string.
19. Light is incident on an analyzer. The transmitted intensity is measured as the orientation of
the analyzer is changed. In each of the following three outcomes, determine whether the
incident light is polarized, partially polarized or completely unpolarized, explaining your
answers.
a. The intensity of the transmitted light is the same no matter what the orientation of the
analyzer.
b. The intensity of the transmitted light varies depending on the orientation of the
analyzer. At a particular orientation, the transmitted intensity is completely zero.
c. The transmitted intensity varies as the orientation varies, but it never becomes zero.
20. State Malus’s Law.
21. Polarized light is incident on a polarizer whose transmission axis makes an angle of 25o
with the direction of the electric field of the incident light. Calculate the fraction of the
incident light intensity that gets transmitted through the polarizer.
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22. Unpolarized light of intensity I o is incident on a polarizer. Calculate, in terms of I o , the
intensity of light transmitted through the polarizer.
23. Calculate the Brewster angle for light incident on a liquid of refractive index of 1.40.
24. Calculate the Brewster angle for light that is
a. Incident on a water-air surface from air
b. Incident on a water-air surface from water
25. A fisherman is fishing in a lake. Explain why it would be easier for him to see the fish in
the lake if he was wearing polarizing sunglasses.
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