CHAPTER 5 NATURE OF WAVES
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1 CHAPTER 5 NATURE OF WAVES 1 Introduction to wave motion Examples of wave motion Two classes of wave: Page 1
2 2 Standard Terminologies for Transverse wave Describing Transverse wave Wave viewpoint Particle viewpoint Amplitude Period Frequency Wavelength Wave speed Page 2
3 3 Equation for wave motion Equation 1: Period and frequency Equation2: Wave equation [wave propagation][hkcee] A vibrator of frequency 5 Hz generates waves on a string. The above diagram shows the shape of the string atthe instant when the vibrator has made one complete vibration. Which of the following shows the waveform 0.1safter? Page 3
4 [State of motion][hkcee modified] A water wave travels toward the right. The diagram above shows the waveform at a certain instant. Write down the states of motion at this instant for particles P, Q and R. [wave propagation][hkcee] A vibrator generates a travelling wave on a string. The above diagram shows the shape of the string at a certaininstant. Which of the following shows the shape of the string between PQ after a quarter of a period? Page 4
5 [Wave motion][hkcee] A vertical vibrator generates waves on a string. It takes 0.25 s to produce a complete wave of wavelength 0.8 m on the string. (a) Find the frequency and speed of the waves on the string. (3 marks) (b) Figure 6 shows the shape of the string at the instant when the vibrator has made one completevibration. (i) At the instant shown, which of the particles A, B, C, D is/are (1) moving downwards? (2) at rest? (ii) Sketch the shape of the string after s, showing the position of the particles A, B, C and D.(6 marks) Page 5
6 4 Graphs of wave motion Displacement-distance graph [Concept] The figure below shows a wave on a string travelling to the right at time t=0s. The wave has amplitude of 3 cm and period of 2 s. Draw the displacement-distance graph at time t=0.5s, locating the points P and Q on the graph. Displacement-time graph Draw the displacement-time graph for the particle at P, from t=0sto t=5s. Page 6
7 [Displacement graph][hkcee] A train of water waves is generated in a ripple tank. The above graph shows the variation of the displacement of a cork placed in the water with time. Find the frequency of the waves. A. 0.2 Hz B Hz C. 4 Hz D. 5 Hz E. 10 Hz [Displacement graph][hkcee] Five corks are moving up and down on the surface of a pond as a water wave passes through them. At time t = 0,the positions of the corks are shown above. The right figure shows the displacement-time graph of one of thefive corks. Which cork has the motion represented by the graph? (Note: Displacement is positive when the cork is above the still water surface.) A. P B. Q C. R D. S E. T Page 7
8 FINAL REMARKS This is an introductory chapter for the later discussion of wave motion, which focuses on describing the various characteristics of waves. Students should have a solid understanding about the concepts of wavelength, amplitude, frequency and period of a wave. The most important equation in this chapter is the wave equation, v= fλ, which applies to any kind of wave motion. The displacement-distance and displacement-time graphs look very similar; however they have very different meaning to a wave: while the former looks at the wave as a whole at a particular instant, the latter give the motion of a particle on a wave through time at a particular position. Students should differentiate between them. APPENDIX 1: PHASE RELATIONSHIP [Concept] Write down the phase relationship for particles (a) P&T (b) P&R (c) Q&S Page 8
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