1. Wave Motion

2. Wave Types Longitudinal –Motion parallel to energy transport Transverse –Motion perpendicular to energy transport

3. Properties of Waves Wavelength –, distance between crests Frequency –f, # oscillations per second Speed –How quickly the disturbance moves Equilibrium A

4. CDR Radio What is the wavelength of CDR Radio? For FM stations the call numbers is the frequency of the station in megahertz f = 90.3×10 6 Hz Velocity for radio waves is the same as the speed of light. v = 3.0×10 8 m/s

5. Time Dependence A moving function has both time and position dependence. y = f(x-v·t) (travel to the right) y = f(x+v·t) (travel to the left) Ex. Haar Wavelet 0 m1 m2 m-1 m-2 m T = 2s T = 0s

6. Wave Number Time dependent wave Wave number k is to as  is to T Another form

7. Wave velocity Ex. What is the velocity of a wave pulse on a 1 mm diameter Copper wire w/ tension of 230 N? (  cu = 8.92 × 10 3 kg/m 3 ) Waves on a String T = Tension  = mass/length

8. Sound Waves Compression (High Pressure) Rarefaction (Low Pressure) Frequency Ranges –Infrasonic < 20 Hz –Audible 20 – 20k Hz –Ultrasonic > 20k Hz Equil. Comp. Rare.

9. Speed of Sound Air –Bulk modulus (B) - How easy it is to compress a volume of air. –At 20°C and sea level v = 343 m/s (air) Solids –Young’s modulus (Y) - How easy it is to compress a solid.

10. Sound Level Intensity - Power transmitted per unit area. Intensity Level – Perceived intensity of sound. –Measured in decibels (dB) –10 times the intensity is perceived as plus 10 dB –2 times the intensity is perceived as plus 3 dB Threshold of hearing, I 0 = 10  12 W/m 2 (Spherical Wave)

11. Fireworks 100 m away from an explosion the intensity level is 120 dB. What is the intensity level at 500 m?

12. The Ear Mechanical energy is converted into a neural signal in the cochea. –Nerve cells are triggered by the displacement of the basilar membrane.

13. Superposition Principle When 2 or more waves are present, the resulting wave is an algebraic sum of all the waves. Interference Constructive - Waves in phase + A -A A 2A -2A + A -A A 2A -2A Destructive - Waves 180° out of phase

14. Adding Waves At t = 0s, the crests of two waves are located at the origin. If the first wave has an amplitude of 5 cm and wavelength of 2 m and the second wave has an amplitude of 2 cm and a wavelength of 0.5 m, what does the resulting wave look like?

15. Beats Periodic variation in intensity with two waves close in frequency. From Trig: Therefore, Modulation Envelope Oscillate Average freq.

16. Beat Frequency One speaker is transmitting a 10 Hz signal and a second is transmitting a 11 Hz signal. What beat frequency is experienced?

17. Interference Remember the Superposition Principle Constructive Destructive #1 #2 r1r1 r2r2 Source Effect

18. Earthquakes S waves – Transverse –Shear P waves – Longitudinal –Compression Northridge, CA 1994

19. Standing Waves Two identical waves traveling in opposite directions. Antinodes - Max Amplitude Nodes - Zero Amplitude

20. Harmonic Series Have a node at each end of the string. Possible wavelengths Frequency L n=1 n=2 n=3 fundamental 1st overtone 2nd overtone 1st harmonic 2nd harmonic 3rd harmonic

21. Waves on a String General Form for normal modes –Nth harmonic (n=1, 2, 3, …) Ex. A 4.0 g wire is stretched to its full length of 1.75 meters under a tension of 400 N. What frequency is heard as it vibrates in the wind?

22. Double Open Ended Pipe Air oscillates in and out of the pipe’s ends. (n=1, 2, 3, …) Air Displacement 2nd Harmonic 3rd Harmonic Fundamental

23. Single Open Ended Pipe Air oscillates in and out of the pipe’s ends. (n=1, 3, 5, …) Air Displacement 1st Overtone 2nd Overtone Fundamental

24. Organ Pipe Ex.A pipe organ needs to play a low B b (116.54 Hz). If a single open ended pipe is used, how long should the pipe be? What is the frequency of the 2nd overtone for this pipe?

25. Doppler Effect If a source is stationary wave are emitted radially outward. Wavelength in direction of motion is compressed. Therefore, frequency heard is (v S and v O considered positive when approaching each other)

26. Doppler Effect While standing at a corner, the siren of the police car goes from 530 Hz to 470 Hz as it passes by. How fast is the car traveling? Stationary SourceMoving Source

27. Shock Waves Supersonic speeds –Mach Number –Angle of shock wave v – velocity of sound v s – velocity of the supersonic object vsvs v 