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2/22/06 Waves & The Wave Equation CH 15, #33: neat application, but not really waves. Leave till end Thursday: Computer Exercise #2, meet in Olin 269 (Astro.

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Presentation on theme: "2/22/06 Waves & The Wave Equation CH 15, #33: neat application, but not really waves. Leave till end Thursday: Computer Exercise #2, meet in Olin 269 (Astro."— Presentation transcript:

1 2/22/06 Waves & The Wave Equation CH 15, #33: neat application, but not really waves. Leave till end Thursday: Computer Exercise #2, meet in Olin 269 (Astro Lab) Friday: Chap. 16: Sec. 16-1 thru 16-5

2 Particles vs. Waves Types of Waves Transverse vs. Longitudinal

3 ConcepTest #29: A string is held at one end, while the other end goes over a pulley and is attached to a mass M, as shown. Transverse waves on the string travel with speed v. If the mass M is quadrupled, what is the new wave speed? M 1.0 4. v (remains same) 2.v /45. 2 v 3.v /26. 4 v

4 ConcepTest #30: Two wave machines are hooked together. The wave machine on the left has a wave speed higher than the wave machine on the right. Consider the following choices: a)A wave pulse comes from the left to the right (high speed region to low speed region). Which of the above is correct for the REFLECTED pulse? b) A wave pulse comes from the left to the right (high speed region to low speed region). Which of the above is correct for the TRANSMITTED pulse? 1.Pulse inverted3. No pulse 2.Pulse not inverted4. Not enough info

5 Wave Speed cares about Medium Example: Light Speed in vacuum = c Speed in medium = v Index of refraction n > 1;  larger n, slower speed Wave traveling from one medium into another Speed changes Incident waves splits up into Reflected wave Transmitted wave High speed  Low speed Reflected Wave INVERTED Low speed  High speed Reflected Wave NOT INVERTED Video Demos

6 Mathematical Description of Waves & the Wave Equation  Wave function describes oscillation about equilibrium Examples: position of slinky coil; pressure of air (sound wave); electric field (EM wave) Wave Equation Partial Derivatives Examples: Don’t panic Wave functions? Concentrate on Harmonic Waves

7 Harmonic Waves “snapshot” Fixed position

8 Definitions “snapshot” Fixed position

9 ConcepTest #31:

10 ConcepTest #32: a)What is the amplitude of this wave? b)What is the wavelength of this wave? c)What is the angular frequency of this wave? d)What is the speed of this wave?


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