Homework Book Wave Properties Huijia Physics Homework Book 1 Semester 2 Name: Homeroom: Physics Class:
Week 1 Reflection, Refraction, wave equations 1. If the wavelength of an incident wave is 1.5cm and the frequency of the source is 10Hz, calculate the wavelength of the reflected wave and the speed of the waves. [1 mark] 2. The diagrams below show snapshots of travelling plane wavefronts in different situations. Barrier Sketch a snapshot of each situation to show the wavefronts a short while later. [4 marks] 3. A simple experiment was conducted in order to find the speed of sound. The experimenter stands 40m away from a large wall and begins to clap her hands. The claps are adjusted so that each clap coincides with the echo from the previous clap. The time taken for 10 of these claps was recorded to be 3.5 seconds. Calculate the speed of sound according to this experiment. [2 marks] 4. The diagram below shows the displacement with time of a particle of medium through which a wave is travelling. Time (s)
Calculate the following: a. The frequency of the source producing the wave. [1 mark] b. The amplitude of the wave. [1 mark] c. The period of the wave. [1 mark] d. The equation of the oscillation. The mathematical equation of an oscillation is given by: [2 marks] 5. A sailor strikes the side of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0s later. The velocity of a wave in a liquid is given by: ; where B is the bulk modulus of water (B =2.0x10 9 N/m 2 ) and the density of water (ρ= 1.025x10 3 kg/m 3 ). [3 marks] Week 2 Basic Huygens principle, Snell s law, Critical angle, TIR 6. An Earthquake P wave passes across a boundary rock where its velocity increases from 6.5km/s to 8km/s. If it strikes this boundary at 30, calculate the angle of refraction. [2 marks] 7. A sound wave is travelling in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of 25, what is the angle of refraction? Assume that the cold air is 10 C and the warm air temperature is +10 C. The speed of sound as a function of temperature can be approximated by 331 0.60 m/s where T is in C. [3 marks] 8. Explain briefly: a. The difference between a transverse and a longitudinal wave and give one example of each. [1 mark] b. The difference between polarised and un polarised light. [1 mark] c. Why sound cannot be polarised. [1 mark] 9. The table gives the speed of light in different media. Medium Speed of light (m/s) Vacuum 3.00x10 8 Ice 2.29x10 8 Ethanol 2.21x10 8 Quartz 1.94x10 8 a. Calculate the values of the absolute refractive indexes of ice, ethanol and quartz. [2 marks] b. Calculate the refractive index for light travelling from ice into ethanol. [1 mark] c. A piece of ice is placed in ethanol, in which direction is light travelling for total internal reflection to take place? Calculate the value of the critical angle. [2 marks] 10. Light of frequency 6.00x10 14 Hz is incident on an air water boundary at an angle of 63. The speed of light in air is 3.00x10 8 m/s and the speed of light in water is 2.25x10 8 m/s. a. State the laws that describe the refraction of light. [1 mark] b. Calculate the wavelength of the light in air. [1 mark] c. Calculate the refractive index for light passing from air to water. [1 mark] d. Calculate the angle of refraction in the water. [2 marks]
Week 3 Diffraction, Superposition 11. The diagram shows and optical fibre made of a plastic coated glass. The refractive index of the glass is 1.58 and that of the plastic is 1.24. a. Calculate the refractive index for light striking the glass plastic interface. [1 mark] b. Calculate the value of the critical angle at this interface. [1 mark] c. The diagram shows 2 paths of light through the fibre. Explain how this can affect a pulse of light as it passes along the fibre. [2 marks] 12. The diagram shows two pulses in a string travelling towards each other. The width of each pulse is 1cm and they travel at 1cm/s. At the instant shown, they are separated by 1cm. 1cm/s 1cm 1cm 1cm 1cm/s a. Sketch a diagram to show the shape of the string, 0.5s and 1.0s later. [1 mark] b. Explain what has happened to the Energy of the 2 pulses 1.0s later. [1 mark] 13. The diagram below shows the interference pattern in water, of two coherent sources. The dotted lines are troughs and the bold lines are crests of the wave. a. Define, node and anti node. [1 mark] b. Mark on the diagram one point where it is a node and one point that it is an anti node. [1 mark] c. Mark in the lines of constructive and destructive inference. [1 mark]
14. A cellular phone uses a radio wave of 2GHz. What is the smallest size of object that the wave can diffract readily around? [1 mark] 15. A microwave cooker uses an electromagnetic wave of frequency 1GHz, what is the approximate angle of diffraction if an object of 72cm blocks part of the wave. Give your answer in degrees. [1 mark] Week 4 Interference, Beats, Double Slit 16. The diagram shows two identical loudspeakers, A and B, placed 0.75m apart. Each loudspeaker emits a sound of frequency 2000Hz. Point C is on a line midway between the speakers and 5.0m away form the line joining the speakers. A listener at C hears the intensity of sound. If the listener moves from C to E or D, the sound intensity heard decreases to a minimum. Further movement in the same direction results in the repeated increase and decrease in sound intensity. Speed of sound in air is 330m/s. A E 0.75m C B 5.0m D a. Explain why the sound intensity is: i. A maximum at C. [1 mark] ii. A minimum at D or E. [1 mark] b. Calculate: i. The wavelength of the sound. [2 marks] ii. The distance CE. [2 marks] 17. A tuning fork produces a steady 200Hz tone. When this is tuning fork is struck and held near a vibrating guitar string, twenty beats are counted in five seconds. What are the possible frequencies produced by the guitar string? [2 marks] 18. For an observable interference pattern between two sources, the sources must be coherent. What is meant by two coherent sources? What TWO other conditions should be met for an observable interference pattern? [1 mark] 19. Light of wavelength 500nm is incident on two small parallel slits separated by 1.0mm. At what angle is the first maximum formed? If after passing through the slits the light is brought to focus on a screen 1.5m from the slits what is the observed fringe spacing on the screen? [2 marks] 20. Two tuning forks are sounded together, one of frequency 440Hz and the other of frequency 442Hz both with the same intensity. What is the frequency of the sound that is heard, that is twice the intensity of one of the forks? What is the beat frequency? [2 marks]
Week 5 Standing Waves 21. Show that the wavelengths of the standing wave in a string of length L are given by where n is the number of the harmonic. [2 marks] 22. An organ pipe closed at one end produces a fundamental note of frequency 440Hz. a. What are the frequencies of the first two harmonics above the fundamental? [2 marks] b. What would the frequency of the first two harmonics above the fundamental of a pipe of the same length but open at both ends? [1 mark] c. Taking the speed of sound to be 330m/s estimate the length of the pipes. [1 mark] 23. A guitar string is 90cm long and has a mass of 3.6g. The distance from the bridge to the support post is L = 62cm, and the string is under tension 520N. What are the frequencies of the fundamental and first two overtones? [2 marks] 24. The diagram shows how the profile of a wave on a rope changes. In a period of 2.50x10 4 s it moves from position 1 to position 2. Give all necessary answers in degrees. Displacement (m) 0.1 X X Y Z 1 0.1 0 0.6 1.2 1.8 Distance (m) 2 a. Write down the wavelength of the wave. [1 mark] b. Calculate the frequency of the wave. [2 marks] c. Calculate the speed of the wave along the rope. [3 marks] d. How can you tell from the diagram that the wave is a stationary wave? [1 mark] e. Suggest how the stationary wave is formed in this example. [1 mark] What is the phase difference between: f. The two points marked X on the diagram? [1 mark] g. The two points marked Y and Z on the diagram? [1 mark] 25. What will be the fundamental frequency and first overtones for a 26cm long organ pipe if both ends are open? Draw a labelled diagram to show the graphs of vibration. [3 marks]