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

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1 Assignment Waves Reading: Giancoli, Chapters 11, 12, 22, 24 Holt, Chapters 12, 14 Objectives/HW The student will be able to: 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. 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. 3 State the wave type and medium of EMR and sound and identify the speed of each. State and recognize the different types of electromagnetic radiation (EMR): radio, microwave, infrared, light, ultraviolet, x-ray, gamma. State the relation between speed, wavelength, and frequency for a wave, and use this relation to solve related problems. 4 Create the two wave graphs given a wave s parameters and/or determine a wave s parameters given the two graphs. HW: 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. What is the difference between wave frequency and wave velocity? 5. 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? Page 1 of 5

2 6. 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. 7. When a sound wave goes from water to air its speed and wavelength change, but its frequency does not. Explain why the frequency is constant. 8. Suppose a wave enters a medium where its speed is decreased as a result. Explain what will happen to this wave s wavelength and frequency. 9. In the last century, people put their ears to a railroad track to get an early warning of an approaching train. Why did this work? 10. 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? 11. What happens to the wavelength of a radio signal as its frequency is increased? 12. An ocean wave has a length of 10.0 m. A wave passes a fixed location every 2.0 s. What is the speed of the wave? 13. 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? 14. 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? 15. The frequency of yellow light is Hz. Find the wavelength. 16. 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? 17. Compare and contrast mechanical waves and electromagnetic waves noting similarities and differences. 18. (a) AM radio signals are broadcast at frequencies between 550 khz and 1600 khz. What is the range of wavelengths for these signals? (b) Repeat for FM, which ranges from 88 MHz to 108 MHz. 19. 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 its wavelength in air? 20. A sound wave of wavelength 70.0 cm and velocity 330 m/s is produced by a tuning fork that vibrates for 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? Page 2 of 5

3 21. The speed of sound in water is 1498 m/s. A sonar signal is sent from a ship at a point just below the water surface and 1.80 s later the reflected signal is detected. How deep is the ocean beneath the ship? 22. A bolt of lightning occurs 5.00 km away from you. This bolt emits light with wavelength 450 nm and sound with frequency 35.0 Hz. (a) What is the frequency of the light? (b) What is the wavelength of the sound? (c) What amount of time elapses between seeing and hearing the bolt? 23. 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? 24. 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 is the mass/unit length, then the speed, v, is related by the following equation: v 2 = T/. 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 cm? 25. 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? 26. A sound wave with period 80.0 s 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. 27. A marine radar operating at a frequency of 9400 MHz emits groups of radio waves 80.0 ns in duration. (The time needed for reflections of these groups to return indicates the distance of the target.) Radio waves are EMR. (a) Find the wavelength of these waves. (b) Find the length of each wave group, which is indicative of the precision with which the radar can measure distance. (c) Find the number of complete cycles in the group. 28. A certain sound wave is described by the following two graphs: y(x) = 2.00 sin(72.0 x) + sin(120 x) y(t) = 2.00 sin(27000 t) + sin(45000 t) x = distance in meters, t = time in seconds, y = disturbance level in Pascals Set your graphing calculator to Degree 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.) 29. 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. Page 3 of 5

4 30. On graph paper construct the two graphs necessary to completely describe a sinusoidal sound wave with frequency 5.00 khz and amplitude 1.20 Pa. You may wish to graph these first on your calculator and then transfer some points to graph paper. (a) Make a time graph and on the graph label the period and amplitude. (b) Make a distance graph and label wavelength and amplitude. 31. (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,, T, f, and v. For A,, 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. Page 4 of 5

5 Selected Answers a. b. c a. b. c m/s 13. a m/s b s 14. a. 2.4 m/s b. 2.9 m nm m/s a. 190 m 550 m b. 2.8 m 3.4 m 19. a km/s b s c mm 20. a. 471 Hz b. 236 waves c. 165 m m 22. a Hz b m c s km N 25. a. ¼ b s c. 1.4 Hz 26. a cm b khz 27. a cm b m c a. sketch b. sketch 29. a m b s c Hz d m e. 375 m/s 30. a. graph b. graph 31. a. graph with A,, T, f, v b. graph with A,, T, f, v c. graph with A,, T, f, v d. graph with A,, T, f, v Page 5 of 5