Introduction to Waves

1. 0 Introduction to Waves

2. 0 What is a wave? • It is a disturbance that carries energy through matter or space. • Some require a “medium” (the matter in which the a wave travels) • Ex) sound requires matter to travel (air, water, earth, etc.) • Some do not require a medium • Ex) light, radio, and x-rays do not need anything to travel.

3. Wave motion • Motion of mechanical wave (as opposed to electromagnetic wave) due to vibration of particles in a medium • Transverse – vibration of particles perpendicular to direction of wave propagation (wave motion) • Longitudinal – vibration of particles parallel to direction of wave propagation (wave motion) • http://www.cbu.edu/~jvarrian/applets/waves1/lontra_g.htm • Note that a medium is required before a mechanical wave can propagate!

4. 0 Types of Waves • Mechanical Waves- require a medium • Almost all waves are mechanical. • Electromagnetic Waves-don’t require a medium.

5. 0 Transverse Waves • Transverse waves have perpendicular motion. • Light waves travel perpendicularly through space. • The sine function describes their movement.

6. 0 Longitudinal Waves • Longitudinal waves have parallel motion. • The wave causes the medium to vibrate in the same direction as the wave itself. • Ex) earthquakes and sound

7. Basic characteristics of waves Frequency • “how often” (cycles/sec, wiggles/sec, ) Hertz Wavelength • Length of one wave (“S” shape)

8. Physical characteristics of a wave • Frequency (f) – The number of waves produced in 1second Note: units for frequency is hertz or Hz • Period (T) – The time taken to produce one complete wave (ie covers one wavelength) • f • http://www.surendranath.org/Applets.html waves transverse waves

9. 0 Wave Characteristics • Wavelength(): The distance between corresponding point on adjacent waves. • Crest- peak of the wave • Trough- valley of the wave • Amplitude- height of the wave from the origin.

10. Standing Waves:

11. 0 • Frequency (): The number of waves that pass a given point in a specific time, usually one second. Frequency really describes ENERGY! • Units for Frequency— waves/second   • Hertz (Hz) = 1 wave/second

12. 0 Energy Is Involved!!!! • A wave is a disturbance that carries Energy! • This is described by its frequency! • Energy may spread out as a wave travels. • The higher the frequency, the more energy the wave is carrying! E = ħxf frequency Energy of wave Plank constant=6.626 × 10-34 J·s

13. 0 Wavelength is Inversely Proportional to Frequency • A) Wavelength increases (LONG), then frequency decreases. • B) Wavelength decreases (SHORT), then frequency increases

14. 0 The Electromagnetic Spectrum • Electromagnetic waves include disturbances in electric or magnetic fields and does not require a medium. • Light is one kind of electromagnetic wave.

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16. 0 Calculating Wave Speed • wave speed = frequency (f) x wavelength () v = f x 

17. Speed of waves • Recall speed = • So for waves, speed v = distance covered in 1 wavelength time taken to cover 1 wavelength Recall f so speed of waves v = Speed equation for waves v = f l Note that speed of waves  speed of vibration of particles in medium http://www.surendranath.org/Applets.html

18. 0 Sample problem • What is the speed of the wave which has a wavelength 15.0 m and frequency of 0.100 Hz? v = f x  v = (.100 Hz) (15.0 m) = 1.50 m/s

19. Example on Stadium Wave • A stadium wave typically has a wavelength of 5m. If the speed of • the wave that moves round the stadium is 20m/s. Imagine you are • one of the spectators in the crowd. • How many waves do you expect to see being generated per second? • f = v/l So f = 20/5 = 4 Hz • 4 waves are generated per second • How long does it take one wave to be generated? • T = 1/f So T = 1/4 = 0.25s • Given that the total circumference of the stadium is 800m, how long do you have to wait before the next round of wave reaches you? • time taken = distance/speed So wait time = 800/20 =40s

20. 0 Wave Speed Depends Upon The Medium The “Kinetic Theory” explains this: • Gases: molecules are spread far apart and they have to travel great distances before they can transfer the “disturbance” of energy to another molecule. • Liquids: they are free to “slide” past one another. This allows them to transfer their disturbances much more quickly. • Solids: they are tightly packed together and it is very easy for vibrations to be passed to one another. Sound will travel 15 to 20 times faster in rock or metal than air.

21. 0 Wave Speed Depends Upon The Medium

22. 0 Using the pictures of different mediums answer the following questions: • Compare the speed of sound to air at 0 degrees and at 25 degrees. Why does sound travel faster at 25 degrees? • Predict what will happen when air is at 100 degrees.

23. 0 Using the pictures of different mediums answer the following questions: • Why is salt water a better medium that pure water? • Explain why solids will allow sound to travel faster than liquids or gases.

24. 0 Electromagnetic Waves have finite speed • All electromagnetic waves will travel at the same speed in empty space. • c =3 x 108 m/sec • c- is the symbol that represents speed of light.

25. Common Uses for Waves • Radio waves are used to carry signals over large distances • Ultrasound uses very high frequency sound waves to make images of the inside of the body • Light is a wave that has different frequencies we call colors

26. Ripples in water and other applets http://www.falstad.com/ripple/

27. 0 Doppler effect originally discovered by the Austrian mathematician and physicist, Christian Doppler (1803-53) • The Doppler effect, named after Christian Doppler, is the change in frequency and wavelength of a wave that is perceived by an observer moving relative to the source of the waves.

28. 0 Doppler effect • Heard an ambulance go by recently? Remember how the siren's pitch changed as the vehicle raced towards, then away from you? First the pitch became higher, then lower.

29. 0 • As the ambulance approaches, the sound waves from its siren are compressed towards the observer. The intervals between waves diminish, which translates into an increase in frequency or pitch.

30. 0 • As the ambulance recedes, the sound waves are stretched relative to the observer, causing the siren's pitch to decrease. By the change in pitch of the siren, you can determine if the ambulance is coming nearer or speeding away. If you could measure the rate of change of pitch, you could also estimate the ambulance's speed.

31. 0 • By analogy, the electromagnetic radiation emitted by a moving object also exhibits the Doppler effect. The radiation emitted by an object moving toward an observer is squeezed; its frequency appears to increase and is therefore said to be blueshifted. In contrast, the radiation emitted by an object moving away is stretched or redshifted. As in the ambulance analogy, blueshifts and redshifts exhibited by stars, galaxies and gas clouds also indicate their motions with respect to the observer.

32. Red-shift examples 0 • Early in 20th century, astronomers noticed that distant galaxies had peculiar light spectra. Specifically, the galaxies' light spectra were shifted toward the red end of the spectrum. Receding Advancing

33. 0 Cosmological Redshift • Astronomers use Doppler shifts to calculate precisely how fast stars and other astronomical objects move toward or away from Earth. For example the spectral lines emitted by hydrogen gas in distant galaxies is often observed to be considerably redshifted. The spectral line emission, normally found at a wavelength of 21 centimeters on Earth, might be observed at 21.1 centimeters instead. This 0.1 centimeter redshift would indicate that the gas is moving away from Earth at over 1,400 kilometers per second (over 880 miles per second).

34. WAVES Properties Types of mechanical wave Amplitude Wave motion Period T Due to vibration of particles in medium f = 1 / T Transverse Longitudinal Frequency f sound Wavelength l Wave equation v = fl Examples Speed v Ripples in water Stadium wave