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.

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 “ConceptualQuestions,” 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 obeywave equations!

Note: wave speed is alsogiven by ω/k!

Be careful: wave speed is NOT the same asspeed of the particles doing the wiggling! Thelatter quantity is vy = dy/dt and wiggles withtime; the wave speed is CONSTANT, anddetermined by properties of the thing that'swiggling.

Slide 20-89

The Doppler Effect: Moving Source

Doppler shift: general formula

f L=vw±vL

v w∓vS

f S

This gives the frequency shift. L stands for“Listener” and S stands for “Source.” Use theupper signs for motion toward one another, andthe lower signs for motion apart from one another.

Clickers: A rocket-powered Segwaycan move at 1/10th the speed of sound.Which use below will produce the highestheard frequency of a sound made by a source?

a) Source moves toward listenerb) Listener moves toward sourcec) (a) and (b) will produce equal shiftsd) Source moves away from listenere) Listener moves away from source

Clickers: The Doppler shift formulagiven 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 twowaves is also a valid wave. (Ch. 21!)

We can use superpositionin a fancy way in order toexplain why a fixed endreflects a wave pulseupside-down.

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

Standing Waves

(On a string with twofixed ends, or an organpipe 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 21-31

A. 0.25 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 frequenciesare allowed for a string with two free ends?

a) Same as for two fixed ends b) Only odd harmonics of the fixed-end f_1are allowed c) Only even harmonics of fixed-end f_1

areallowed d) All harmonics except n=1 are allowed e) Standing waves would be impossible fortwo free ends.

Standing waves:one free end; onefixed 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 andL_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 twowaves, the distances to the sources and thewavelength λ determine the phases of thewaves at the point in question.