Ch.11 Waves Homework: Concept Questions: 1, 2. Problems: 3, 9, 13, 39, 45, 49. Wave motion, reflection, refraction, interference, diffraction, standing waves. (sections 5, 6)

2 Waves traveling disturbance transport energy (not matter) only longitudinal waves in fluids Transverse Longitudinal

Intensity intensity drops as the inverse square of distance from a point source

Ex. Intensity at 1m = 1W/m^2. Intensity at 0.01m is:

5 Waves on Strings Wave Velocity depends on: tension in string (F) and, the mass per unit length of string. Example: F=36N, m/L=0.010kg/m

6 Periodic Waves continuous, well defined amplitude (A), frequency (f), and wavelength ( ) speed v = f. Example: f = 10 hertz, = 3 m. v = (10/s)(3m) = 30m/s. A A

7 Principle of Superposition when two or more small amplitude waves overlap the net disturbance is the sum of the individual wave disturbances Example: noise cancellation headphones Sound PHET small amplitude waves are unchanged outside the area of overlap

Ex: wave1 has A1 = 0.10m, wave2 has A2 = 0.30m. Each has same f. The minimum and maximum wave amplitudes in an area of overlap are: If they were each 0.3m, the answers would be 0.6m and 0m. If there were three amplitudes, 5m, 1m, and 1m, the answers would be 7m and 3m.

Reflection

Refraction & Diffraction Refraction: wave direction changes due to change in speed, e.g. light entering water changes direction. Diffraction: wave direction changes due to proximity to an object, e.g. waves spread out after passing through a narrow opening.

11 Standing Waves Nodes (places with zero amplitude) wavelength = 2 x (Node to Node distance) Anti-nodes (places with maximum amplitude) Allowed frequencies are called harmonics Clip Vernier Pamp (start at 2 min)Vernier Pamp Waves on String PHET …waves in which the amplitude at a given location does not vary with time. Due to interference of a confined wave.

12 Standing Wave: Both Ends Fixed

Summary Intensity Wave Properties (f,, v, amplitude) Transverse vs. Longitudinal Waves Reflection, Refraction, Interference, and Diffraction Superposition of Waves Standing Waves on a String

14 Standing Wave: One End Fixed, One End Free

Ex1. Transverse Standing Waves on 10m of 4g/m string fixed at both ends. Mass? Stretched to 15m with force of 5N. m/L? Wave speed? Wavelength, frequency of 1 st harmonic? 15

Ex2. A String 10m long has tension 10N and transverse wave speed of 36m/s. Mass of string? The string is stretched to 15m with 20N. What is % increase in speed? 16

Ex3 Slinky Stretch, measure force, estimate distance & speed of transverse waves. Weigh slinky and compute theoretical value of speed of transverse waves for the estimated distance. How do the values compare? 17

18 natural frequency lowest frequency an object vibrates with when struck also called “resonant frequency” Demo: Driving Tuning Fork /

19 resonance absorb max energy: frequency = resonant frequency example: 256 Hz guitar string resonates when exposed to 256 Hz. Chilandi plates video