1. More Waves!

2. Intensity Intensity – the rate at which energy flows through a surface Point source outputs a fixed power, say P 0 Watts

3. Example A 60 W light bulb emits light waves in every direction. If you stand 2 m away and hold up a black sheet of paper that is 10 cm x 20 cm, how much energy does that paper absorb in 1 minute? What if you move to 4 m away?

4. Doppler Effect Stationary source emits sound waves at a given frequency, f s, and wavelength, λ s. Approaching observer detects extra wavefronts each second. Perceived frequency is the sum of the emitted frequency and the extra wavefronts detected per second.

5. Doppler Effect For a stationary observer and a moving source, the equation becomes: If both the observer and the source are moving (along a line), the equations combine to yield: Choose signs so as to yield correct result!

6. Shock waves Wave fronts “bunch up” on forward side of moving source. If v s > v, wavefronts fall on a single, ultra-high intensity line.

7. Shock waves Wave fronts “bunch up” on forward side of moving source. If v s > v, wavefronts fall on a single, ultra-high intensity line.

8. Standing Waves Standing Wave – a wave pattern that does not appear to move These are the ONLY types of waves that can persist on a string. If string is fixed at each end, then the end points must not move (obvious). For a given length of string, L, there are only a few specific wavelengths that will satisfy this condition. Fundamental frequency Harmonics, or overtones n = 5 Guitar, piano, cello…

9. Standing Waves Standing Wave – a wave pattern that does not appear to move These are the ONLY types of waves that can persist on a string. If string is free at each end, then the end points must be points of maximum displacement (less obvious than fixed case, but still true). For a given length of string, L, there are only a few specific wavelengths that will satisfy this condition. n = 3 Same as for fixed ends! Pan flute, clarinet, pipe organ

10. Standing Waves Standing Wave – a wave pattern that does not appear to move These are the ONLY types of waves that can persist on a string. If string is fixed at one end and free at the other end… n = 2 Pipe organ, marimba…

11. Sound “Beats” f 1 = 50 Hz f 2 = 60 Hz

12. Doppler Use – Radar Guns A police radar gun emits electromagnetic waves at a frequency of 36 GHz (36x10 9 Hz). If these waves reflect off of an oncoming car traveling at 50 mph (~25 m/s), what return frequency does the radar gun detect? The speed of electromagnetic waves in air is 3.0x10 8 m/s. There’s a better way!

13. Resonance Resonance occurs when a system with a natural oscillation frequency is driven by a force with the same frequency. When this condition is met, the system oscillates with an increasingly large amplitude.condition