where N is number of cycles, t is time where t is time and N is the number of cycles

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1 Name: Physics 11 H. Date: Section 2-. The Wave Equation How are waves produced? Waves are produced by a wave pulse. A wave pulse is a single disturbance that travels through a medium (water, air, glass, etc..) A traveling wave is a series of wave pulses at regular intervals. Key Terms for Waves Symbol = Unit = Frequency - the number of complete waves produced per second. Symbol = f Units = (Named after Henry Hertz who discovered radio waves) Formula: where N is number of cycles, t is time Formula Period - time taken to produce one complete wave. Symbol = T Units = seconds (s) Formula: where t is time and N is the number of cycles Amplitude - the greatest displacement of the wave away from its undisturbed position. Think of the amplitude as the height of a hump. Phase - a description of a stage that a periodic motion has reached, usually by comparison with another such motion of the same frequency. Two varying quantities are said to be in phase if their maximum and minimum values occur at the same instant. Example: Indicate the interval that represents one full wavelength. a. A to C c. A to G b. B to D d. C to G Why would we need to know the speed of a wave anyway? To predict when a tsunami will strike the shore.

To determine the epicentre of an earthquake. To do this, seismologists look at the difference in time it takes for a P-wave to reach a location and an S-wave to reach a location.

2 To determine the epicentre of an earthquake. To do this, seismologists look at the difference in time it takes for a P-wave to reach a location and an S-wave to reach a location. Wave speed = wavelength x frequency Example1: What is the speed of a sound wave if its frequency is 256 Hz and its wavelength is 1.29 m? Solution: Example2: suppose a wave has a wavelength of 5.0 m, and that it takes 0.20 sec for one wavelength to pass a given point. Then in this case, = 5.0 m, T = 0.20 s, and Example3: Two men are fishing from small boats located 30 m apart. Waves pass through the water, and each man s boat bobs up and down 15 times in 1.0 min. At a time when one boat is on a crest, the other one is in a trough, and there is one crest between the two boats. a) Find the frequency of the waves. b) Determine their wavelength. c) What is the speed of each wave? Waves at Boundaries What does the speed of a wave depend on? The speed of a wave does not depend on the. The speed of a wave depends on the in which it travels. THIS IS A PROPERTY OF THE MEDIUM NOT THE WAVE (LIKE BOILING POINT, DENSITY, ETC) What does the speed of a wave depend on? The forces between the particles of the medium The mass of the particles of the medium Question: Which of the two pulses (C or D) will travel from the hand to the wall in the least amount of time? Justify your answer

3 Reflection of Waves from Boundaries Waves carry energy and momentum, and whenever a wave encounters an obstacle, they are reflected by the obstacle. This reflection of waves is responsible for echoes, radar detectors, and for allowing standing waves which are so important to sound production in musical instruments. Incident Wave: Transmitted Wave: Reflected Wave: Wave that does not move to the but backward from the boundary If the medium, the amplitude of the transmitted wave will be almost as large as the incident wave. Most of the energy If the medium is, most of the wave energy will be Wave Boundary Less Dense to More Dense Medium The reflected wave is inverted. The denser medium has a smaller amplitude and wavelength (less energy). The frequency does not change. Interference What happens when 2 waves pass through the same region of space at the same time When waves do interact with each other, the phenomenon is called Types of Interference When 2 crests arrive at the same time The 2 crests move the wave upwards to make a larger wave (temporary) When 1 crest and 1 trough arrive at the same time and cancel each other out if they are identical in size (temporarily). Partially destructive waves may not cancel each other but dampen the wave temporarily.

Figure 2 Figure 3 Figure 2: This is an example of what is called. Notice that crests are twice as high and troughs are twice as deep. Figure 3: The two sets of waves exactly cancel each other.

Blue Wave Green Wave Both Waves 6 4 6 4 6 4 2 2 0-2 -4 2 + 0-2 -4-6 = -4-6 -6 1st dot: Amplitude = 0 + 2 = 3rd dot: Amplitude = + = 0-2 2nd dot: Amplitude = + -2 = 4th dot: Amplitude = + = What is

4 Figure 2 Figure 3 Figure 2: This is an example of what is called. Notice that crests are twice as high and troughs are twice as deep. Figure 3: The two sets of waves exactly cancel each other. This is an example of. Blue Wave Green Wave Both Waves = st dot: Amplitude = = 3rd dot: Amplitude = + = 0-2 2nd dot: Amplitude = + -2 = 4th dot: Amplitude = + = What is the principle of superposition? Example 2 of Superposition If one wave has an amplitude of +3cm and the other wave has an amplitude of +6cm, the resultant displacement is Law of Reflection r i Normal line (perpendicular to barrier) When a wave strikes a barrier, the angle from the normal line at which it strikes the barrier and the angle from the normal at which it is reflected are equal i r =

5 Name: Physics 11 H. Date: Wave - Assignment #2 1. Several positions along the medium are labeled with a letter. Categorize each labeled position along the medium as being a position where either constructive or destructive interference occurs. 2. Explain, with the help of a sketch, what each of these terms means with respect to waves: (a) crest; (b) trough; (c) wavelength; (d) frequency; (e) amplitude. 4. How are frequency and period related? 5. A dog wags its tail 50 times in 20 s. What are (a) the frequency and (b) the period of vibration of the tail? 6. What is the difference between a transverse wave and a longitudinal wave? 7. For any kind of wave motion, how are wave speed, wavelength and frequency related to one another? 8. Alternating current in power lines produces electromagnetic waves of frequency 60 Hz that travel outward at the speed of light, which is 3.0 x 10 8 m/s. What is the wavelength of these waves? 9. If the speed of sound is 330 m/s, what wavelength does a sound of frequency 512 Hz have? 10. Name at least three properties of light that can be explained adequately with a wave theory. 11. Explain the difference between refraction and diffraction. Give an example of each phenomenon from everyday experience. 12. When waves slow down on entering a new medium, what happens to (a) their wavelength? (b) their frequency? and (c) their direction? Under what conditions will the direction not change? 13. What is (a) constructive interference? (b) Destructive interference? 14. A sound wave produced by a clock chime is heard 515 m away 1.50 s later. a. a. What is the speed of the sound of the clock s chime in air? 343 m/s b. b. The sound wave has a frequency of 436 Hz. What is the period? 2.3 x 10-3 s c. What is the wavelength? m

6 15. A hiker shouts toward a vertical cliff 685 m away. The echo is heard 4.00 s later. a. a. What is the speed of sound of the hiker s voice in air? 171 m/s b. b. The wavelength of the sound is m. What is the frequency? 228 cycles/s c. c. What is the period of the wave? 4.4 x 10-3 s 16. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of m? 1.5 m/s 17. The speed of a transverse wave in a sting is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz. What is its wavelength? 3.0 m 18. Five pulses are generated every s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm? f= 50 pulses/s, v = 60. cm/s or 0.60 m/s (the latter is better!) 19. A periodic longitudinal wave that has frequency of 20.0 Hz travels along a coil spring. If distance between successive compressions is m, what is the speed of the wave? 8.0 m/s Wave Behaviour Problems 1. If waves maintain a constant speed, what will happen to their wavelength if the frequency of the waves is (a) doubled? Half (b) halved? Doubled 2. What is the frequency of a sound wave if its speed is 340 m/s and its wavelength is 1.70 m? 200 Hz 3. Waves of frequency 2.0 Hz are generated at the end of a long steel spring. What is their wavelength of the waves travel along the spring with a speed of 3.0 m/s? 1.5 m 4. A student measures the speed of water waves in her tank to be 25 cm/s. If the wavelength is 2.5 cm, what is the frequency of the waves? 10 Hz 5. The speed of light is 3.0 x 10 8 m/s. What is the frequency of light waves if their wavelength is 600 nm? (1 nm = 10-9 m) Consult a spectrum chart to see what colour of light this would be. 5.0 x Hz (green) 6. Some microwaves have a frequency of 3.0 x Hz. How long is a microwave of the frequency? (Microwave radiation travels at the speed of light.) m 7. Five pulses are generated every s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm? 0.60 m/s 8. Bill counts 5 waves on a pond in 10 s. The distance between them is 80 cm. What is their speed? 9. Lizi reads the back label of her microwave oven. It says frequency = 2,450 MHz. The speed of microwaves is m/s. What wavelength are they? 10. Paul plays a note of wavelength 25 cm on his synthesiser. He knows the speed of sound is 340 m/s in air. What is its frequency?

v = fλ PROGRESSIVE WAVES 1 Candidates should be able to :

v = fλ PROGRESSIVE WAVES 1 Candidates should be able to : PROGRESSIVE WAVES 1 Candidates should be able to : Describe and distinguish between progressive longitudinal and transverse waves. With the exception of electromagnetic waves, which do not need a material