AP Physics 1 Assignment – Waves & Interference

Reading
Sections: 11-7 thru 11-12, 12-1, 12-4 thru 12-7, Giancoli
Sections: 16.9 thru 16.11, 17.1 thru 17.3, 17.5 thru 17.7, Open Stax College Physics

Objectives/HW

	The student will be able to:	HW:
1	Define, apply, and give examples of the following concepts: wave, pulse vs. continuous wave, source, medium, longitudinal wave, transverse wave, surface wave, crest, trough, compression, rarefaction.	1 – 11
2	Define, apply and give examples of the following wave parameters: speed, wavelength, frequency, period, and amplitude and state the influence of source and medium on each wave parameter.	1 – 11
3	Identify the wave type, medium, and speed of mechanical waves and sound. State the relation between speed, wavelength, and frequency for a wave, and use this relation to solve related problems.	12 – 18
4	Solve problems analyzing graphs to determine a wave’s parameters.	19 – 21
5	Define and apply the following concepts: superposition, constructive and destructive interference, phase, beat frequency and solve related problems.	22 – 24
6	Explain the requirements for the creation of a standing wave. Define and identify nodes and antinodes in standing wave patterns. Solve problems involving harmonics for strings or pipes.	25 – 38
7	Define resonance and identify and give examples of this phenomenon.	39 – 41

Homework Problems

1. What are the differences and similarities among transverse, longitudinal, and surface waves?

2. Suppose an astronaut standing on the Moon rings a metal bell. Would that astronaut hear the bell? How about any other astronauts in the vicinity? Explain.

3. Suppose an earthquake occurs in California. The resulting seismic waves are recorded by special equipment (seismographs) in laboratories all over the world (not just in California). (a) What is the source of seismic waves? (b) What is the medium of seismic waves? (c) Scientists use measurements of seismic waves to map out and determine the properties of the Earth’s interior – explain how the Earth’s interior might affect the seismic waves.

4. Suppose you produce a transverse wave by shaking one end of a spring back and forth. How does the frequency of your hand moving back and forth compare with the frequency of the wave that travels down the spring? Explain.

5. A physics teacher creates waves that travel along a spring that is stretched across the room. (a) Without changing the length of the spring, can the teacher change the speed of the waves in the spring? Explain. (b) Can the teacher change the frequency of the waves in the spring? Explain. (c) Can the teacher change the wavelength of the waves in the spring? Explain.

6. An ocean wave has a wavelength of 10.0 m. A complete wave passes a fixed location every 2.0 s. What is the speed of the wave?

7. Water waves in a shallow dish have troughs that are 6.0 cm apart. At one point in the dish the water is observed to undergo 4.8 oscillations up and down every second.
(a) What is the speed of these waves? (b) What is the period of these waves?

8. Water waves in a lake travel 4.4 m in 1.8 s. The period of the oscillation is 1.2 s.
(a) What is the speed of these waves? (b) What is the wavelength?

9. A group of swimmers is resting in the sun on a raft. They estimate that 3.0 m separates a trough and an adjacent crest of surface waves on the lake (these must be physics students!). They count 14 crests that pass by the raft in 20.0 s. How fast are the waves moving?

10. The velocity of the transverse waves produced by an earthquake is 8.9 km/s, while that of the longitudinal waves is 5.1 km/s. A seismograph records the arrival of the transverse waves 73 s before that of the longitudinal waves. How far away is the earthquake that produced the two types of waves?

11. The velocity of a wave on a string depends on how hard the string is stretched, and on the mass per unit length of the string. If T is the tension in the string, and m is the mass/unit length, then the speed, v, is related by the following equation: v² = T/m. A piece of string 5.30 m long has a mass of 15.0 grams. What must the tension of the string be to make the wavelength of a 125 Hz wave equal 120.0 cm?

12. A sonar signal of frequency 1.00 MHz has a wavelength of 1.50 mm in water. (a) What is the speed of the signal in water? (b) What is its period in water? (c) What is would be its wavelength in air moving at speed of sound 343 m/s?

13. When a sound wave goes from water to air its speed and wavelength change, but its frequency does not. (a) Explain why the frequency is constant. (b) If the speed increases what must happen to the wavelength going from air to water? Explain.

14. Suppose you hear the sound made by a certain tuning fork. And then you hear the sound made by the same tuning fork but the room’s temperature is higher than before. How do the speed, wavelength, and frequency of this sound at higher temperature compare to the speed, wavelength, and frequency at lower temperature?

15. A sound wave of wavelength 70.0 cm and speed 330 m/s is produced by a tuning fork that vibrates for 0.500 s. (a) What is the frequency of the tuning fork? (b) How many complete waves are emitted from the tuning fork in this time interval? (c) For this group of waves, how far is the front wave from the back wave?

16. The speed of sound in water is 1498 m/s. A sonar signal of frequency 225 kHz is sent from a ship at a point just below the water surface and 1.80 s later the reflected signal is detected. (a) How deep is the ocean beneath the ship? (b) How many complete cycles will “fit” between the ship and the ocean floor?

17. The time needed for a water wave to change from the equilibrium level to the crest is 0.18 s. (a) What fraction of a cycle is this? (b) What is the period of the wave?
(c) What is the frequency of the wave?

18. A sound wave with period 80.0 ms goes from air to water. The speed of sound in water is 1498 m/s. (a) Find the change in the wavelength. (b) Find the frequency of sound heard by an underwater listener.

19. A certain sound wave is described by the following two graphs:
y(x) = 2.00 sin(2π x/5) + sin(2π x/3)
y(t) = 2.00 sin(150π t) + sin(250π t)
x = distance in meters, t = time in seconds, y = disturbance level in Pascals
Set your graphing calculator to Radian mode and graph the above equations one at a time. You will need to adjust your viewing window for each graph. (a) Make a sketch of the distance graph showing the wave’s shape. (b) Make a sketch of the time graph showing the wave’s shape. (These do not have to be graphed on graph paper!)

20. Use the tracing features of your calculator and any necessary calculations to determine the following parameters for the sound wave of the previous problem:
(a) Wavelength, (b) Period, (c) Frequency, (d) Amplitude, (e) Speed.

21. (a) through (d) – Turn in the 4 pairs of graphs that were done (or started) in class. For each pair of graphs you should indicate A, λ, T, f, and v. For A, λ, and T, you should label how you found the values on the graphs. For f and v, you should show the calculations you made to find them.

22. Suppose two sine waves are produced – each with wavelength 10.0 m. One wave has amplitude 7.00 cm and the other has amplitude 2.00 cm. Determine the wavelength and amplitude of the superposition of these two waves: (a) if the two waves are exactly in phase, and (b) if the two waves are exactly out of phase.

23. A radio receiver is prone to a phenomenon known as multipath interference. In this case, the radio signal coming from a broadcast tower reflects off of various obstacles and takes different (or multiple) paths to the receiver’s antenna. (a) Explain how this can result in poor reception. (b) Explain how it could possibly improve reception.

24. A guitarists tunes his A-string to 220.0 Hz by comparing it to a sound known to have that frequency. (a) If he hears beats at a frequency of 2 Hz and his string is sharp (pitch is too high) what is the frequency of the string? (b) If it is desired to get within 219.9 to 220.1 Hz simply by listening it will be necessary to hear beats with what period?

25. Explain what is happening at a node in a standing wave produced in a guitar string.

26. An organ pipe involves standing waves that occur in the air inside it. What would happen to the pitch of the pipe if the temperature of the air increases? Explain!

27. An organ pipe that is covered at one end produces a certain note. If the cover is removed from the end what will happen to the pipe’s pitch? Explain!

28. A standing wave is produced in a thin strip of metal at a frequency of 125 Hz. The nodes in the pattern are 5.00 cm apart. For the waves in the metal strip find the following: (a) wavelength, and (b) speed.

29. A certain skyscraper is 440 m tall and is found to sway back and forth with a period of 10.0 seconds. A simple model of this phenomenon would be to assume the building is like a huge standing wave where the base of the building is like a node and the top of the building is like an anitnode. If this is the case what is the speed of waves traveling up and down the building?

30. A string 45.0 cm long is fixed at both ends to a musical instrument. Waves in the string travel at speed 520 m/s. Sketch the standing wave, find the frequency and wavelength for each of the following: (a) the fundamental, (b) the 2^nd harmonic, (c) the 3^rd harmonic.

31. A 12.0 cm pipe is open at both ends. Sketch the standing wave, find the frequency and wavelength for each of the following: (a) the 2^nd harmonic, (b) the 3^rd harmonic.

32. A violin string is 25.4 cm long and produces a fundamental frequency of 440.0 Hz (an A). The violinist frets the string to change the length of the string. This changes the fundamental. (a) What is the speed of waves in the string? (b) What change in length is required to produce a frequency of 523 Hz (a C)? (c) At its new length what wavelength of sound is produced by the violin?

33. A 0.560 m pipe is closed at one end. Sketch the standing wave, find the frequency and wavelength for each of the following: (a) the fundamental, (b) the next possible harmonic.

34. A slide whistle has a length of 27 cm. If you want to play a note one octave higher (twice the frequency), the whistle should be how long?

35. If you hold a 1.2 m aluminum rod in the center and hit one end with a hammer, it will oscillate like an open pipe. The speed of sound in aluminum is 5150 m/s. What would be the lowest frequency at which the rod will vibrate when it is hit?

36. A flute acts like an open pipe and sounds a note with a 370 Hz pitch. What are the frequencies of the four lowest pitched harmonics that the flute makes?

37. A clarinet sounds the same note as in the previous problem, 370 Hz. It, however, behaves the same as a pipe that is closed off at one end. What are the frequencies of the four lowest pitched harmonics that the clarinet makes?

38. An opera singer can cause a crystal glass to shatter just by the sound of her voice. However this only works if the singer hits a certain note and not other notes.
(a) Explain why the glass shatters at a certain note. (b) Explain why the glass does not shatter at other notes that are just as loud.

39. I drive an old, kind of pathetic, cheap car. When I accelerate various things will rattle. For example the sun visors might start buzzing when I hit 30 mph. But then when I get to 35 mph the visors will stop buzzing and the glove box will start rattling. And then when I get to 40 mph the glove box stops rattling and some mysterious piece of loose metal somewhere hidden deep behind the dash will start humming. And so on. Explain what is going on here in terms of a source of vibration, standing waves, and resonance. (And be happy if your car doesn’t do this!)

40. A kid plays around with a 76 cm tube of wrapping paper pretending that it is a horn or a megaphone. However, in reality, the tube can actually serve to amplify the sound of the kids voice. Determine two frequencies at which the tube will resonate.

41. An open vertical tube is filled with water and a tuning fork vibrates over its mouth. As the water level is lowered in the tube, resonance is heard when the water level has dropped 17 cm and again after 51 cm of distance exists from the water to the top of the tube. What is the frequency of the tuning fork?

Selected Answers

3.a.

5. a.

6. 5.0 m/s

7. a. 0.29 m/s

b. 0.21 s

8. a. 2.4 m/s

b. 2.9 m

9. 4.2 m/s

10. 870 km

11. 63.7 N

12. a. 1.50 km/s

b. 1.00 ms

c. 0.343 mm

13. a.
b.

14.

15. a. 471 Hz

b. 236 waves

c. 165 m

16. a. 1350 m
b. 203000

17. a. ¼

b. 0.72 s

c. 1.4 Hz

18. a. 9.24 cm

b. 12.5 kHz

19. a. sketch

b. sketch

20. a. 15.0 m

b. 0.0400 s

c. 25.0 Hz

d. 2.77 m

e. 375 m/s

21. a. graph with A, l, T, f, v

b. graph with A, l, T, f, v

c. graph with A, l, T, f, v

d. graph with A, l, T, f, v

22. a.
b.

23. a.
b.

24. a. 222 Hz
b. 10 s

25.

26.

27.

28. a. 10.0 cm

b. 12.5 m/s

29. 176 m/s

30. a. 578 Hz, 0.900 m

b. 1160 Hz, 0.450 m

c. 1730 Hz, 0.300 m

31. a. 2860 Hz, 0.120 m

b. 4290 Hz, 0.080 m

32. a. 224 m/s

b. – 4.0 cm

c. 65.6 cm

33. a. 153 Hz, 2.24 m

b. 459 Hz, 0.747 m

34. 13.5 cm

35. 2100 Hz

36. 370 Hz, 740 Hz, 1110 Hz, 1480 Hz

37. 370 Hz, 1110 Hz, 1850 Hz, 2590 Hz

38. a.

39.

40. any two multiples of 226 Hz

41. 500 Hz