Chapter 11 General Waves Properties

Chapter 11 General Waves Properties

Learning Outcomes

After completing this chapter, students should be able to:

1. describe what is meant by wave motion as illustrated by vibrations in ropes and springs and by waves in a ripple tank

2. show understanding that waves transfer energy without transferring matter 3. defme speed, frequency, wavelength, period and amplitude 4. state what is meant by the term wavefront 5. recall and apply the relationship velocity = frequency x wavelength to new situations or to solve related

problems 6. compare transverse and longitudinal waves and give suitable examples of each

11.1 Describing Wave Motion page 171 l. Energy transfer often involves the net movement of matter but for wave motion it does not.

2. Stretch a long spring or rope between two students. One can transmit energy to the other without transferring matter.

3. Point out to students that their ear drums are being moved (vibrated) without the transfer of matter.

4. Describe what is meant by wave motion as illustrated by vibrations in ropes and springs and by experiments using a ripple tank.

5. Use ripple tanks to show water waves transferring energy. A small piece of cork vibrates as the wave passes. Compare with sound and hearing.

Answer to Think Time question page 171

Energy is transferred.

11.2 Transverse and Longitudinal Waves page 172 l. Describe transverse and longitudinal waves in such a way as to illustrate the differences between them.

2. Use the long spring to show transverse waves. Introduce the terms crest and trough.

3. Use the long spring to show longitudinal waves. Introduce the terms compression and rarefaction.

4. Examples of longitudinal waves include sound, ultrasound, seismic P-waves and shock waves.

Answers to Section Review questions page 174

1. A wave is a phenomenon in which energy is transferred through vibrations.

2. Light is an example of transverse wave and sound is an example of longitudinal wave. Transverse waves are waves which travel in a direction perpendicular to the direction of the vibrations. Longitudinal waves are waves which travel in a direction parallel to the direction of vibrations.

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Chapter 11 General Waves Properties

11.3 Wave Terms page 174 1. Define the terms amplitude, wavelength, period, frequency and speed and deduce the formula for

speed.

2. Do calculations using speed = frequency x wavelength. Use the formula to deduce the speed of radio waves from the published wavelength and frequency of a local station.

3. Explain the term "wavefront". The wavefront may be a line or a surface.

Answer to Think Time question page 175

The wavelength of a longitudinal wave is the distance between successive compressions or rarefactions.

11.4 Graphical Representation of Waves page 176 1. Emphasise that the displacement of wave is a function of both position and time.

2. The graphs to be plotted are displacement-position graph and displacement-time graph.

3. The two graphs may look alike. To identify them, check the x-axis of the graph.

Answers to Section Review questions page 179

1. Frequency = _1_ period

2. Speed = frequency x wavelength

3. Wavelength .2 Period T

4cm 0.2s 0.1 m 5 ms 8m 0.08 s

Frequency! Speed v 5 Hz 20 cm S ·l

200Hz 20 ms ·1

12.5 Hz lOOms

Physics in Society: Quantum Mechanics page 180 Answers to Q

1. Classical Physics consists mainly of Newtonian Mechanics and Maxwell's theory of electromagnetism.

2. It explains many puzzling experimental data much better than classical physics.

3. The intense curiosity to unveil the mysteries of nature and the strong collaboration among the closely­knit scientific community help to build a firm foundation in quantum mechanics.

4. The benefits include many areas of computerized automation in transportation, in industries, and in devices used at home and at work.

Answers to Misconception Analysis page 181, 182

1. False. 2. True 3. False. 4. True 5. True 6. False. 7. False. 8. False. 9. True. 10. True.

Waves transfer energy but vibrations do not

This is true for longitudinal wave but not true for transverse wave.

Amplitude is half the distance between the crest and a trough The longer the period, the lower is the frequency The higher the frequency , the shorter is the wavelength

The period is obtained from the graph and frequency is then determined.

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Chapter 11 General Waves Properties

Answers to Multiple Choice Questions page 182, 183

1. D 2. B 3. D v = fl. = 8 Hz x 2 em = 16 m S-I 4. D 5. B A= 2x4m = 8m

v 8ms-' f= -= --= 1 Hz A. 8 m

v 12ems-' 6. B A= -= = 4em

f 3Hz

7. C v = fl. A. 8 em -I

8. B v = fl. = - = -- = 2 em s T 4s

1 1 9. A f = -= -= 0.5 Hz

T 2s

Answers to Structured Questions page 183

1. (a) v = fl. = 600 Hz x 0.5 m = 300 m S-I

(b) f = ~ = 300ms-' =375Hz A. 0.8m

2.

(e) A = 2'.. = 300 m S-I 0.30 m f 1000Hz

gem (a) Wavelength = -- = 1.5 em

6 gem -I

(b) Speed = -- = 3 em s 3s

v 3ems-1

(e) f = - = ~ = 2 Hz A. 1.) em

3. v = fl. = 500 Hz x 0.2 m = 100 m S-I

T· ak distanee 400 m -_ 4 s Imet en = ---speed 100 m S-l

4. A- ~ - 300ms-1

= 0.60 m f 500Hz

Number of waves = length = 600 m = 1000 wavelength 0.6 m

5. v = fl. = 3 Hz x 12 em = 36 em S-l

6. f = 30 Hz 1m

A= -=0.02m 50

v = fl. = 30 Hz x 0.02 em = 0.6 m S-1

7. (a) (i) Amplitude = 0.6 m

.. 7m (u)Wavelength = 2 = 3.5 m

Answers to Critical Thinking Questions page 183

1. A small eork vibrates up and down as water wave passes. This shows that water waves earry energy.

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Chapter 11 General Waves Properties

2. The horizontal displacement of each coil from its equilibrium (zero) position is measured. Displacement to the right is taken as positive displacement and displacement to the left is taken as the negative displacement.

3. The 'human wave' generated is a transverse wave. The longitudinal wave can also be formed with the people moving left and right.

Extension page 183

1. Oscillating Water Column (OWC), e.g. 'Limpet' (Land Installed Marine Powered Energy Transformer) and 'Sperboy'- a partly submerged structure (,collector') open to the sea below the water surface so that it contains a column of water. Air is trapped above the surface of the water column. As waves enter and exit the collector, the water column moves up and down and acts like a piston on the air, pushing it back and forth. The air is channelled towards a turbine and forces it to turn. The turbine is coupled to a generator to produce electricity. Overtopping, e.g. 'Wave Dragon ' - a structure over which the waves topple, a reservoir to collect the water and hydro turbines installed at the bottom of the reservoir. The head of collected water turns the turbines as it flows back out to sea and the turbines are coupled to generators to produce electricity. Point absorber, e.g. the 'AquaBuOY', 'PS Frog' and 'Wavebob' - This is a floating structure that absorbs energy in all directions by virtue of its movements at or near the water surface. Terminator - This is also a floating structure that moves at or near the water surface, but it absorbs energy in only a single direction. The device extends in the direction normal to the predominant wave direction, so that as waves arrive, the device restrains them. Attenuator, e.g. the 'Pelarnis' - This device is a long floating structure like the terminator, but is orientated parallel to the waves rather than normal to them.

Refer to websites: http://en.wikipedia.org/wiki/Wave_power httlp://www.darvill.clara.neUaltenerg/wave.htm http://www.carbontrust.co . ukltechnology/technologyacceleratorlME~uide.htm#1

2. Body Waves Body waves travel through the interior of the Earth. The first kind of body wave is the P wave or primary wave. This is the fastest kind of seismic wave. In air, P waves travel at the speed of sound. Typical speeds are 330 m S-I in air, 1450 m S-I in water and about 5000 m S- I in granite. P waves can move through solid rock and fluids, like water or the liquid layers of the Earth. It pushes and pulls the rock it moves through. It is a longitudinal wave.

The second type of body wave is the S wave or secondary wave, which is the second wave you feel in an earthquake. An S wave is slower than a P wave and can only move through solid rock. This wave moves rock up and down, or side-to-side. It is a transverse wave.

P waves shake the ground in the direction they are propagating, while the slower S waves shake perpendicularly or transverse to the direction of propagation.

Surface Waves The first kind of surface wave is called a Love wave after a British mathematician who worked out the mathematical model for this kind of wave in 1911. It is the fastest surface wave and moves the ground from side-to-side.

The other kind of surface wave is the Rayleigh wave named after another British mathematician who predicted its existence in 1885. A Rayleigh wave rolls along the ground just like a wave rolls across a lake or an ocean. Because it rolls, it moves the ground up-and-down and side-to-side in the same direction that the wave is moving. Most of the shaking felt from an earthquake is due to the Rayleigh wave, e.g. cars moving up and down as the wave passes on the road surface below them.

Refer to websites: http://www.geo.mtu.eduIUPSeis/waves.htrnl http://www.seismo.um . ed ulftp/pub/louie/class/IOO/seismic-waves.htrnl http://en.wikipedia.org/wiki/Seismic_wave

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