Phys. 122: Thursday, 03 Sept. HW 1 returned: please pick up yours in front. Written HW 2: due by 2:00 pm. Written HW 3: ch. 21, probs. 8, 27, and 62, and ch. 22, probs. 6, 18, and 38. Due in one week. Written HW reminder: Assigned problems are the “Exercises and Problems,” NOT the “Conceptual Questions,” which often (confusingly) have the same numbers. Mast. Phys.: Assign. 1 due Tuesday evening. Reading: Finish ch. 22 by Tuesday (you may skip sections 22.5 and 22.6, and “intensity” in 22.2).

(WAS: Clickers: why are waves important?) a) They're not. b) All things have wavelike behavior. c) Waves which obey quantum mechanics look like particles. d) Conservation of energy and momentum is secretly just conservation of wave phase. e) All of (b)-(d) are true. As far as we know, all truly elementary particles (e.g. electrons, photons, the quarks inside nuclei) are quantum excitations of “fields” which obey wave equations!

Note: wave speed is also given by ω /k! Be careful: wave speed is NOT the same as speed of the particles doing the wiggling! The latter quantity is v y = dy/dt and wiggles with time; the wave speed is CONSTANT, and determined by properties of the thing that's wiggling.

Slide The Doppler Effect: Moving Source

Doppler shift: general formula This gives the frequency shift. L stands for “Listener” and S stands for “Source.” Use the upper signs for motion toward one another, and the lower signs for motion apart from one another.

Clickers: A rocket-powered Segway can move at 1/10th the speed of sound. Which use below will produce the highest heard frequency of a sound made by a source? a) Source moves toward listener b) Listener moves toward source c) (a) and (b) will produce equal shifts d) Source moves away from listener e) Listener moves away from source

Clickers: The Doppler shift formula given applies to all waves except which of the following? a) Sound waves in solids b) Water surface waves c) Light and other electromagnetic waves d) Transverse waves on a stretched string e) Sound waves in fluids

Superposition: the sum of any two waves is also a valid wave. (Ch. 21!)

We can use superposition in a fancy way in order to explain why a fixed end reflects a wave pulse upside-down.

... and also why a “free” end reflects a wave pulse right-side up.

Standing Waves (On a string with two fixed ends, or an organ pipe with two fixed ends, etc.): f_n = n f_1...with f_1 = v/(2L)‏ and n = 1,2,3,...

What is the wavelength of this standing wave? QuickCheck 21.3 Slide A m. B. 0.5 m. C. 1.0 m. D. 2.0 m. E. Standing waves don’t have a wavelength.

Clickers: Which standing wave frequencies are allowed for a string with two free ends? a) Same as for two fixed ends b) Only odd harmonics of the fixed-end f_1 are allowed c) Only even harmonics of fixed-end f_1 are allowed d) All harmonics except n=1 are allowed e) Standing waves would be impossible for two free ends.

Standing waves: one free end; one fixed end f_n = n f_1 f_1 = v/(4L)‏ n = 1, 3, 5,... (Odd harmonics only!)‏

Clickers: if two speakers at distances L_1 and L_2 are emitting waves in phase, where will they combine to make a bigger wave? a) Where L_1 + L_2 is a multiple of λ. b) Where L_1 - L_2 is a multiple of λ. c) Where L_1 + L_2 is an odd multiple of λ /2. d) Where L_1 - L_2 is an odd multiple of λ /2.

Basics of Interference (of any type of wave: light, sound, surf,...): If there are only two waves, the distances to the sources and the wavelength λ determine the phases of the waves at the point in question.