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Lecture 10: Phasors and Standing Waves
February 24, 2026
Reading Assignment
- Read: 14.7-14.8; 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)
Objectives
- (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 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.
Homework
- Wednesday's Assigned Problems:
A32, A33, A34, A112, Problem X10; CH 14: 32, 34,
35; Supp CH 1: 1, 2
Answers: CH 14 #32 every 7.5 seconds
- Monday's Hand-In Problems:
A35, A37; CH 14: 36, 70; Supp CH 1: 3
Note: this is only the first half of the hand-in set.
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - 4; CT2 - 2; CT3 - 3; CT4 - 4; CT5 - 3
- Spreadsheet showing the addition of two waves.
Videos of example problems
To 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.- Standing waves on a string.
- Organ pipe that is (a) open on both ends, and (b) open on one end and closed on the other.
- Drawing phasor diagrams
Pre-Class Entertainment
- Cap In Hand - The Proclaimers
- How Sweet It Is (To Be Loved by You) - Marvin Gaye
- Oye Como Va - Santana
- Hand In My Pocket - Alanis Morissette
- Happy - The Rolling Stones