Topic 4: Waves 4.2 Traveling waves
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1 Crests and troughs Compare the waves traveling through the mediums of rope and spring. CREST TROUGH TRANSVERSE WAVE COMPRESSION RAREFACTION LONGITUDINAL WAVE
2 Wave speed and frequency The speed at which a crest is moving is called the wave speed. This is really a measure of the rate at which a disturbance can travel through a medium. Since the time it takes a crest to move one complete wavelength (λ) is one period (T), the relation between v, λ and T is v = λ / T relation between v, λ and T Finally frequency f measures how many wave crests per second pass a given point and is measured in cycles per second or Hz. Again, f = 1 / T. f = 1 / T relation between f and T
3 Solving wave speed and wavelength problems CM PRACTICE: A spring is moved in SHM by the hand as shown. The hand moves through 1.0 complete cycle in 0.25 s. A metric ruler is placed beside the waveform. (a) What is the wavelength? (b) What is the period? (c) What is the wave speed?
4 Solving wave speed and wavelength problems CM PRACTICE: A spring is moved in SHM by the hand as shown. The hand moves through 1.0 complete cycle in 0.25 s. A metric ruler is placed beside the waveform. (a) What is the wavelength? λ = 4.7 cm = m. (b) What is the period? T = 0.25 s. (c) What is the wave speed? v = λ / T = / 0.25 = 0.19 m s -1.
5 EXAMPLE: Graph 1 shows the variation with time t of the displacement d of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. (a) Use the graphs to determine the amplitude of the wave motion.
6 Either graph gives the correct amplitude. EXAMPLE: Graph 1 shows the variation with time t of the displacement d of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. (a) Use the graphs to determine the amplitude of the wave motion. Amplitude (maximum displacement) is m.
7 EXAMPLE: Graph 1 shows the variation with time t of the displacement d of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. (b) Use the graphs to determine the wavelength.
8 EXAMPLE: Graph 1 shows the variation with time t of the displacement d of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. (b) Use the graphs to determine the wavelength. Graph 2 must be used since its horizontal axis is in cm (not seconds as in Graph 1). Wavelength is measured in meters and is the length of a complete wave. λ = 2.40 cm = m.
9 EXAMPLE: Graph 1 shows the variation with time t of the displacement d of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. (c) Use the graphs to determine the period.
10 EXAMPLE: Graph 1 shows the variation with time t of the displacement d of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. (c) Use the graphs to determine the period. Graph 1 must be used since its horizontal axis is in s (not cm as in Graph 2). Period is measured in seconds and is the time for one complete wave. T = 0.30 s.
11 EXAMPLE: Graph 1 shows the variation with time t of the displacement d of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. (d) Use the graphs to find the frequency.
12 EXAMPLE: Graph 1 shows the variation with time t of the displacement d of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. (d) Use the graphs to find the frequency. This can be calculated from the period T. f = 1 / T = 1 / 0.30 = 3.3 Hz. [3.333 Hz]
13 EXAMPLE: Graph 1 shows the variation with time t of the displacement d of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. (e) Use the graphs to find the wave speed.
14 EXAMPLE: Graph 1 shows the variation with time t of the displacement d of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement d. (e) Use the graphs to find the wave speed. This can be calculated from λ and T. v = λ / T = / 0.30 = m s -1.
15 PRACTICE: Graph 1 shows the variation with time t of the displacement y of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement. (a) Use the graphs to determine the amplitude and wavelength of the wave motion.
16 PRACTICE: Graph 1 shows the variation with time t of the displacement y of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement. (a) Use the graphs to determine the amplitude and wavelength of the wave motion. Graph 2 must be used for λ since its horizontal axis is in cm. Amplitude (maximum displacement) is y = m. Wavelength is y = 0.30 cm =.0030 m.
17 PRACTICE: Graph 1 shows the variation with time t of the displacement y of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement. (b) Use the graphs to determine the period and the frequency.
18 PRACTICE: Graph 1 shows the variation with time t of the displacement y of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement. (b) Use the graphs to determine the period and the frequency. Period (cycle time) is 0.25 ms = s. Frequency is f = 1 / T = 1 / = 4000 Hz. Graph 1 must be used for T since its horizontal axis is in ms.
19 PRACTICE: Graph 1 shows the variation with time t of the displacement y of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement. (c) Use the graphs to determine the wave speed..
20 PRACTICE: Graph 1 shows the variation with time t of the displacement y of a traveling wave. Graph 2 shows the variation with distance x along the same wave of its displacement. (c) Use the graphs to determine the wave speed. Wave speed is a calculation. v = λ / T = / = 12 m s -1.
21 EXAMPLE: Graph 1 shows the variation with time t of the displacement x of a single particle in the medium carrying a longitudinal wave in the +x direction. (a) Use the graph to determine the period and the frequency of the particle s SHM.
22 EXAMPLE: Graph 1 shows the variation with time t of the displacement x of a single particle in the medium carrying a longitudinal wave in the +x direction. (a) Use the graph to determine the period and the frequency of the particle s SHM. The period is the time for one cycle. T = 0.20 s. f = 1 / T = 1 / 0.20 = 5.0 Hz.
23 EXAMPLE: Graph 2 shows the variation of the displacement x with distance d from the beginning of the wave at a particular instant in time. (b) Use the graph to determine the wavelength and wave velocity of the longitudinal wave motion.
24 EXAMPLE: Graph 2 shows the variation of the displacement x with distance d from the beginning of the wave at a particular instant in time. (b) Use the graph to determine the wavelength and wave velocity of the longitudinal wave motion. λ = 16.0 cm = m. v = λ / T = / 0.20 = 0.80 m s -1.
25 EXAMPLE: Graph 2 shows the variation of the displacement x with distance d from the beginning of the wave at a particular instant in time. (c) The equilibrium positions of 6 particles in the medium are shown below. Using s, indicate the actual position of each particle at the instant shown above.
26 EXAMPLE: Graph 2 shows the variation of the displacement x with distance d from the beginning of the wave at a particular instant in time. (d) In the diagram label the center of a compression with a C and the center of a rarefaction with an R. C R
27 Students will be expected to derive c = f λ v = λ / T f = 1 / T relation between v, λ and T relation between f and T From the above relations we get: v = λf v = λ / T v = λ(1 / T) v = λf. relation between v, λ and f EXAMPLE: A traveling wave has a wavelength of 2.0 cm and a speed of 75 m s-1. What is its frequency? Since v = λf we have 75 =.020f or f = 3800 Hz.
28 The nature of electromagnetic waves All of us are familiar with light. But visible light is just a tiny fraction of the complete electromagnetic spectrum. The Electromagnetic Spectrum Microwaves Ultraviolet Light Gamma Rays Radio, TV Cell Phones Infrared Light X-Rays Frequency f / Hz Wavelength λ / nm
29 The nature of electromagnetic waves In free space (vacuum), all electromagnetic waves travel with the same speed v = m s-1. We use the special symbol c for the speed of light. c = λf relation between c, λ and f where c = m s-1 PRACTICE: The wavelength of a particular hue of blue light is 475 nm. What is its frequency? Wavelength λ / nm
30 The nature of electromagnetic waves In free space (vacuum), all electromagnetic waves travel with the same speed v = m s-1. We use the special symbol c for the speed of light. c = λf PRACTICE: The wavelength of a particular hue of blue light is 475 nm. What is its frequency? 1 nm is m so that λ = m. c = λf so that = ( )f. f = Hz. relation between c, λ and f where c = m s Wavelength λ / nm
31 The nature of electromagnetic waves c = λf PRACTICE: The graph shows one complete oscillation of a particular frequency of light. (a) What is its frequency, and what part of the spectrum is it from? relation between c, λ and f where c = m s-1
32 The nature of electromagnetic waves c = λf PRACTICE: The graph shows one complete oscillation of a particular frequency of light. relation between c, λ and f where c = m s-1 (a) What is its frequency, and what part of the spectrum is it from? SOLUTION: From the graph T = s. Then f = 1 / T = 1 / s = Hz. This is from the ultraviolet part of the spectrum.
33 The nature of electromagnetic waves c = λf PRACTICE: The graph shows one complete oscillation of a particular frequency of light. (b) What is the wavelength of this light wave? relation between c, λ and f where c = m s-1
34 The nature of electromagnetic waves c = λf PRACTICE: The graph shows one complete oscillation of a particular frequency of light. (b) What is the wavelength of this light wave? relation between c, λ and f where c = m s-1 SOLUTION: All light has the same speed c, so we don t need the x vs. d graph. From c = λf we have λ = c / f. Thus λ = c / f = / = m.
35 The nature of electromagnetic waves c = λf PRACTICE: The graph shows one complete oscillation of a particular frequency of light. (c) Determine whether or not this light is in the visible spectrum Wavelength λ / nm relation between c, λ and f where c = m s-1
36 The nature of electromagnetic waves c = λf PRACTICE: The graph shows one complete oscillation of a particular frequency of light Wavelength λ / nm relation between c, λ and f where c = m s-1 (c) Determine whether or not this light is in the visible spectrum. SOLUTION: The visible spectrum is from about 400 nm to 700 nm. λ = m = m = 180 nm. NO! UV.
37 The nature of electromagnetic waves A ringing bell is placed inside a bell jar, and can be heard to ring. As air is removed from the sealed jar with a vacuum pump, the sound of the ringing bell diminishes until it cannot be heard. The medium through which the sound wave travels has been removed. Thus sound waves cannot propagate through vacuum. But the demonstration also shows that light can propagate through a vacuum. How so?
38 The nature of electromagnetic waves Because light is a wave, scientists believed it needed a medium. They postulated that empty space was not really empty, but was infused with a light-wave carrying medium called the luminiferous ether. Eventually, the results of the Michelson-Morley experiment showed that light waves do not need a physical medium through which to travel. As we will learn in Topic 5, a moving charge produces a changing electric field, which produces a changing magnetic field, and the two fields propagate through vacuum at the speed of light c = ms -1.
39 4.4 Wave behavior Wave behavior PRACTICE: A sound pulse entering and leaving a pocket of cold air (blue). What wave behavior is being demonstrated here? T or F: The period changes in the different media. T or F: The frequency changes in the different media. T or F: The wavelength changes in the different media. T or F: The wave speed changes in the different media. T or F: The sound wave is traveling fastest in the warm air.
40 4.4 Wave behavior Wave behavior PRACTICE: What wave behavior is being demonstrated here? Refraction. T or F: The period changes in the different media. T or F: The frequency changes in the different media. T or F: The wavelength changes in the different media. A sound pulse entering and leaving a pocket of cold air (blue). T or F: The wave speed changes in the different media. T or F: The sound wave is traveling fastest in the warm air.
41
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