# 4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES HW/Study Packet

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1 4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES HW/Study Packet Required: READ Hamper pp SL/HL Supplemental: Cutnell and Johnson, pp , Tsokos, pp REMEMBER TO. Work through all of the example problems in the texts as you are reading them Refer to the IB Physics Guide for details on what you need to know about this topic Refer to the Study Guides for suggested exercises to do each night First try to do these problems using only what is provided to you from the IB Data Booklet Refer to the solutions/key ONLY after you have attempted the problems to the best of your ability UNIT OUTLINE I. DIFFERENT TYPES OF WAVES A. TRANSVERSE AND LONGITUDINAL WAVES B. WAVE PULSES AND TRAVELLING WAVES C. SOUND AND WATER WAVES II. DEFINING TERMS III. GRAPHS OF WAVES A. DISPLACEMENT-TIME GRAPHS B. DISPLACEMENT-POSITION GRAPHS IV. WAVEFRONTS AND RAYS V. ELECTROMAGNETIC (EM) WAVES A. THE WAVE EQUATION FOR EM WAVES B. THE ELECTROMAGNETIC SPECTRUM VI. WHEN WAVES HIT BOUNDARIES BETWEEEN TWO MEDIA A. REFLECTION AND TRANSMISSION B. SNELL S LAW VII. WHEN WAVES INTERACT WITH EACH OTHER A. THE SUPERPOSITION PRINCIPLE B. CONSTRUCTIVE AND DESTRUCTIVE INTERFERENCE C. INTERFERENCE: PATH AND PHASE DIFFERENCE VIII. DIFFRACTION A. WHEN WAVES GO AROUND OBSTACLES B. WHEN WAVES GO THROUGH APERTURES FROM THE IB DATA BOOKLET 1

2 WHAT YOU SHOULD BE ABLE TO DO AT THE END OF THIS TOPIC State what is meant by wave motion, and distinguish between longitudinal and transverse waves Distinguish between a wave pulse and a continuous progressive (travelling) wave Define amplitude, displacement, intensity, wave speed, wavelength, period, and frequency and state the relationship between them Define and identify crest and trough on a graph Define and differentiate between compression and rarefaction Find amplitude and period from a displacement-time graph Find amplitude and wavelength from a displacement-position graph Define waves in two dimensions, and define and differentiate between a wavefront and a ray Apply the wave equation State that all EM waves travel at the same speed in free space, and recall the orders of magnitude of wavelengths of important EM spectrum bands State the principle of linear superposition and apply it to waves and pulses to find resultant waves Describe the reflection and transmission of waves at boundaries, apertures, and obstacles State the laws of reflection and refraction Understand the index of refraction and be able to apply Snell s Law for light Define diffraction and be able to recognize conditions under which it occurs Identify conditions in which two waves will interfere constructively and destructively Explain the role of path difference in the phenomenon of interference HOMEWORK PROBLEMS: 1. A stone is thrown into a still water surface and creates a wave. A small floating cork 1.0 m away from the impact point has the following displacement-time graph (time is measured from the instant the stone hits the water). Find: a) the amplitude of the wave [2.0 cm] b) the speed of the wave [0.67 m s -1 ] c) the frequency of the wave [3.3 Hz] d) the wavelength of the wave [0.20 m] 2. A sound wave from a loudspeaker travels from air into water. The frequency of the sound does not change, because the loudspeaker producing the sound determines the frequency. The speed of sound in air is 343 m/s, whereas the speed of sound in fresh water is 1482 m/s. When the sound wave enters the water, does its wavelength increase, decrease, or stay the same? Explain. 2

3 3. The first 2 graphs below show displacement and position of a wave on a string at two different times (the first graph is the earlier one). The third graph shows the same wave on a string as a graph of displacement and time. Determine: a) The amplitude of the waves [0.6 cm] b) The wavelength of the waves [0.5 cm] c) The period of the waves [4.0 ms] d) The frequency of the waves [250 Hz] e) Speed of the waves [125 cm s -1 ] f) The time elapsed between the first graph and the second graph [80 ms] 4. A source produces water waves of frequency 10 Hz. The graph shows the variation with horizontal position of the vertical displacement of the surface of water at one instant in time. vertical displacement / cm horizontal position / cm 0.4 What is the speed of these water waves? [20 cm s -1 ] 3

4 5. A wave is travelling along the surface of some shallow water in the x-direction. The graph shows the variation with time t of the displacement d of a particle of water. Use the graph to determine for the wave: a) the frequency [7.7 Hz] b) the amplitude [8 mm] c) the wavelength, if the speed of the wave is 15 cm s -1. [2.0 cm] d / mm t / s The graph in #5 shows the displacement of a particle at the position x = 0. On the axes to the right, draw a graph to show the variation with distance x along the water surface of the displacement d of the water surface at time t = s. d / mm x/cm A ray of light in air passes successively through parallel sided layers of water and glass. If the angle of incidence in air is 60.0 degrees, calculate the following. Draw a diagram in the box provided with a straightedge and protractor. a) the angle of refraction in the water [40.6 ] AIR WATER b) the angle of incidence at the water - glass boundary [40.6 ] GLASS c) the angle of refraction of the glass. [34.7 ] 4

5 8. A ray of light is incident on a boundary between glass and air as shown. Express the refractive index of glass in terms of the given variables. [sinθ 4 /sinθ 1 ] 9. The diagram shows two wave pulses at time t = 0. The markings on the x-axis are 1 m apart. Draw a series of y-x graphs (5-6) at one second intervals to illustrate their superposition until after they have crossed. [Hint: sketch the two pulses in lightly and then add the displacements to find the resultant pulse.] 10. Consider the two points P and Q marked on the diagram of question 9. a) Draw a graph showing the displacement b) Draw a second graph to show how the of the point Q from t = 0-6 s as the wave displacement of P varies from t = 0-6 s. pulses pass and separate. 5

6 11. Complete the following sketches them to show what happens when: a) circular waves hit a straight reflector b) straight waves pass from medium 1 into medium 2 in which they travel more slowly c) straight waves meet a small obstacle 12. The diagram shows a series of waves as might be produced in a laboratory experiment with a ripple tank. The waves are travelling from region A to region B and the diagram is shown to scale. a) Describe the phenomenon occurring along the dotted line. A b) By measurement, determine the wavelength of the waves in region A and region B. B c) What can you say about the frequency of the waves in region A and region B? d) What can you say about the speed of waves in region A and region B? e) Where is the water deepest in region A or region B? Explain your reasoning. 13. Two coherent point sources S 1 and S 2 emit spherical waves as shown (lines represent crests). Describe the relative intensity of the waves at P and Q and explain your reasoning. [P: maximum, Q: minimum] 6

7 14. Water waves of wavelength 2.0 m are produced by two sources S 1 and S 2. The sources vibrate in phase. S 1 S 2 1 m 3 m P Point P is 1 m from S 1 and 3 m from S 2. S 1 alone and S 2 alone each produce a wave of amplitude a at P. Determine, in terms of a, the amplitude of the resultant wave at point P when S 1 and S 2 are both emitting waves. [2a] 15. A small sphere, mounted at the end of a vertical rod, dips below the surface of shallow water in a tray. The sphere is driven vertically up and down by a motor attached to the rod. The oscillations of the sphere produce travelling waves on the surface of the water. The diagram below shows how the displacement of the water surface at a particular instant in time varies with distance from the sphere. The period of oscillation of the sphere is s. a) Use the diagram to calculate, for the wave, (i) the amplitude. [1.0 mm] (ii) the wavelength. [6.0 mm] (iii) the frequency. [37 Hz] (iv) the speed. [0.22 m s -1 ] 7

8 b) The wave moves from region A into a region B of shallower water. The waves move more slowly in region B. The diagram (not to scale) shows some of the wavefronts in region A. (i) With reference to a wave, distinguish between a ray and a wavefront. (ii) The angle between the wavefronts and the interface in region A is 60. The quantity n B /n A (the ratio of refractive indices n B to n A ) is 1.4. Determine the angle between the wavefronts and the interface in region B. [38 ] (iii) On the diagram above, construct three lines to show the position of three wavefronts in region B. c) Another sphere is dipped into the water. The spheres oscillate in phase. The diagram shows some lines in region A along which the disturbance of the water surface is a minimum. The frequency of oscillation of the spheres is increased. State and explain how this will affect the positions of minimum disturbance. 8

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