Simple harmonic motion (vibrations) Displacement x=Xcos(wt), x=Xsin(wt) or x=Xcos(wt+f) Occurs if the force on a mass is spring-like

Simple harmonic motion (vibrations) image from hyperphysics

t, secs Amplitude X= ___ Period T = ______ Frequency f = __________ cycles/sec (Hz) Angular frequency w=2pf=_________ (rad/sec)

P1. A mass attached to a spring oscillates back and forth as indicated in the position vs. time plot below. At point P, the mass has A. positive v and positive a. B. positive v and negative a. C. negative v and positive a. D. negative v and negative a. E. positive v and zero a.

Mass on a spring Simple pendulum Frequency, period: Mass all at one distance Does period depend on amplitude?  

“Physical” Pendulum Mass spread out over some distance

A trapeze artist swings on a long trapeze and takes 5 A trapeze artist swings on a long trapeze and takes 5.0 seconds to return to his starting spot. P2. How long will it take a lighter woman of the same height to make the same swing? A: longer B: shorter C the same P3. How long does it take for the artist to go from start to bottom of the swing? ____ sec A: 1.00 B: 1.25 C: 1.75 D. 2.50

Waves Transverse—The disturbance is perpendicular to the direction of the wave. Longitudinal—The disturbance is in the same direction as the direction of the wave Slinky rope sound: gas sound: solids light

Water surface waves

Speed, frequency and wavelength

Waves What a wave “carries” matter? energy? momentum?

Why do some waves go faster than others? Waves in matter almost always obey: Wave speed on string, rope or cable Important in string instruments

P4. Two guitar strings of the same length have the same tension, but one has four times the mass of the other. The speed of a wave on the heavier guitar string is __________ than the lighter string. 2x smaller 4x smaller the same 2x larger 4x larger

Sound Audible sound waves - 20 Hz to 20 kHz (Varies in each person) 1. Canal 2. Eardrum 3. Hammer 4. Anvil 5. Stirrup 6. Oval window 8. Cochlea 9. Nerve of hearing Hearing test! Demo: speaker, frequency source

Speed of sound in a gas or liquid B is the bulk modulus (stiffness of compression) Air: v = 331 m/s at 0 C. Other T’s: v= 331 m/s At 20 C: v = 343 m/s Helium: 972 m/s at 0 C rair/rHe Water: 1500 m/s

Speed of sound in a solid P5. The speed of sound in solids and liquids is faster than in gas because a) solids have greater density b) solids have lower density c) solids have greater stiffness d) solids have lower stiffness