|<Previous||January | February | March | April | May||Next>|
Lecture 10: Phasors and Standing Waves
February 20, 2018
- Read: 14.6--14.7; Supplementary Reading Ch 1.1--1.2
- Study: Ex 14.6; Supp. Fig. 1.4
- Ignore: Eq 14.13 (it's not wrong -- just too specialized to be useful)
- (Continuing objective) Describe applications of the concepts of induction, waves, and light to everyday ``real life'' situations.
- Given a specific expression for a traveling transverse or longitudinal harmonic wave in sinusoidal or complex exponential form, determine amplitude, angular frequency, frequency, wavenumber, wavelength, period, phase shift and wavespeed.
- Correctly sketch phasor diagrams to represent an oscillating system at various times.
- Calculate the beat period and frequency for two signals differing slightly in frequency.
- For standing wave modes on strings or in air columns in pipes: sketch the wave pattern, identify nodes and antinodes, and determine wavelength, wave-number, frequency or wave speed. Write down the complex exponential expression for a given standing wave.
- Wednesday's Assigned Problems:
A32, A33, A34, A92, A112, X3 (CLICK HERE); CH 14: 38, 39; Supp CH 1: 1, 2
Answers: CH 14 #38 (a) 4 m, (b) 14 Hz
- Monday's Hand-In Problems: A35, A37, A88, A104; CH 14: 40, 68; CH 32: 34; Supp CH 1: 3, 4, 6
- Click here for the Lecture overheads.
- Click here for the Wave on a string simulation. To set up the standing wave we did in class, switch the mode to "oscillate", use an amplitude of 0.03, a frequency of 1.5 Hz, turn damping to "None", tension to "Medium", and select "Fixed End". Play around with other frequencies that would allow you set up other modes. You can also try the "Loose End" option and see what you would need to change to get a standing wave set up.
Videos of example problemsTo see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.
- Example #1: Standing waves on a string.