1 / 25

Announcements

Announcements. Final exam is on Monday, April 28 th 3:30-5:30 PM Comprehensive with about 20-25% from Units 19-24 All MC Must earn at least 25% to pass class Section 001 – S BEH AUD Section 006 – FMAB AUD Next Friday, April 25

carl
Télécharger la présentation

Announcements

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Announcements • Final exam is on Monday, April 28th 3:30-5:30 PM • Comprehensive with about 20-25% from Units 19-24 • All MC • Must earn at least 25% to pass class • Section 001 – S BEH AUD • Section 006 – FMAB AUD • Next Friday, April 25 • Professor Gerton will be available for consultation ALL DAY in the Browning Building (Geology/Geophysics) near the 2 Creek Coffee House. Discounted drinks will be available (coffee, hot chocolate, etc.) • We are trying to set up review sessions for that day also: stay tuned.

  2. Lecture 23: Harmonic Waves and the Wave Equation Today’s Concept: Harmonic Waves

  3. What is a Wave? A wave is a traveling disturbance that transports energy but not matter. Examples: Sound waves (air moves back & forth) Stadium waves (people move up & down) Largest in history??? Water waves (water moves up & down) Light waves (what moves?)

  4. Types of Waves Transverse: The medium oscillates perpendicular to the direction the wave is moving. This is what we study in Physics 2210. Longitudinal:The medium oscillates in the same direction as the wave is moving.

  5. From sinusoidal function to traveling wave Start with a drawing of θ -π π 2π -2π

  6. From sinusoidal function to traveling wave Start with a drawing of • Write angle as a function of position: • Wavelength: • Wave number:

  7. From sinusoidal function to traveling wave Start with a drawing of • Write angle as a function of position: • Wavelength: • Wave number: Shift the wave by adding a “phase angle”:

  8. From sinusoidal function to traveling wave Start with a drawing of • Write angle as a function of position: • Wavelength: • Wave number: Shift the wave by adding a “phase angle”: Let the phase angle vary in time:

  9. From sinusoidal function to traveling wave Multiply by an amplitude to give physical dimensions: y A

  10. Wave Properties Amplitude: The maximum displacement Aof a point on the wave. λ A Wavelength: The distance λbetween identical points on the wave. Period: The time Pit takes for an element of the medium to make one complete oscillation.

  11. λ Wave speed vs. Rope speed Imagine we have a sinusoidal wave on a rope: A If then gives: A) The horizontal speed of the wave. B) The vertical speed of a segment of rope. This is the speed of a segment of rope at position xand time t.

  12. λ Wave speed vs. Rope speed Imagine we have a sinusoidal wave on a rope: A To find the speed of the wave, first pick out a distinctive feature of the wave (e.g., a peak). That feature corresponds to a particular value of the cosine (or sine) function, which does not change in time: Constant in time

  13. ACT y = f (x-vt) If a function moving to the right with speed vis described by f (x - vt) then what describes the same function moving to the left with speed v? y y y v x x x 0 0 y A)y = - f (x - vt) v B)y = f (x + vt) x 0 C) y = f (-x +vt)

  14. y y y 0 v x x x y v x 0 Suppose the function has its maximum at f (0). y x – vt = 0 v y = f (x - vt) x =vt x 0 x – vt = 0 v A) y = - f (x - vt) x = vt x + vt = 0 v x =-vt B) y = f (x +vt) -x + vt = 0 v x = vt C) y = f (-x + vt) Moves to the right when the signs in front of the x and t terms are different Moves to the left when the signs in front of the x and t terms are the same

  15. CheckPoint: Wave Equation We have shown that the functional form y(x,t) = Acos(kx-ωt) represents a wave moving in the +xdirection. y A x Which of the following represents a wave moving in the –x direction? A) y(x,t)=Acos(ωt– kx) B) y(x,t)=Asin(kx– ωt) C) y(x,t)=Acos(kx+ ωt) A) y(x,t) =Acos(ωt-kx)I have no clue but this is the only answer with a “-” in front of the x. Plus, its derivative, velocity, is negative so that helps with my reasoning. C) y(x,t) = Acos(kx+ ωt)As the wave reaches its amplitude, kx+wt=0; which means if t is increasing constantly at all times then x must increase constantly in the - direction as well.

  16. How to make a Function Move Suppose we have some function y = f (x): y f(x - a) is just the same shape moveda distance a to the right: x 0 x = a y Let a =vtThen f(x -vt) will describe the same shape moving to the right with speed v. v x 0 x = vt y x 0

  17. Harmonic Wave Consider a wave that is harmonic in x and has a wavelength ofλ. y Now, if this is moving to the right with speed vit will be described by: v x λ y A x If the amplitude is maximum atx = 0 it has the functional form:

  18. Transverse Wave on a String

  19. Energy

  20. CheckPoint: Wave Frequency 2 y A x y B x Waves A and Bshown above are propagating in the same medium with the same amplitude. Which one carries the most energy per unit length? A) A B) B C) They carry the same energy per unit length

  21. CheckPoint Results: Wave Frequency 2 y A x y B x Which one carries the most energy per unit length? A) A B) BC) Same Also, vwave is the same for both: So:

  22. Homework Problem

  23. Homework Problem

  24. Homework Problem

  25. Homework Problem Average speed = distance traveled / time taken Distance traveled by a piece of rope during one period is 4A

More Related