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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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 thru 16-5

Particles vs. Waves Types of Waves Transverse vs. Longitudinal

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 v (remains same) 2.v /45. 2 v 3.v /26. 4 v

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

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

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

Harmonic Waves “snapshot” Fixed position

Definitions “snapshot” Fixed position

ConcepTest #31:

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?