Presentation on theme: "Simple Harmonic Motion. Simple harmonic motion (SHM) refers an oscillatory, or wave-like motion that describes the behavior of many physical phenomena:"— Presentation transcript:
Simple harmonic motion (SHM) refers an oscillatory, or wave-like motion that describes the behavior of many physical phenomena: –a pendulum –a bob attached to a spring –low amp. waves in air, water, the ground –vibration of a plucked guitar string
Objects undergoing SHM trace out sine waves where the d is pos and neg with time.
Velocity and acceleration in SHM The position of an object undergoing SHM changes with time, thus it has a velocity The velocity of an object is the slope of its graph of position vs. time. Thus, we can see that velocity in SHM also changes with time, and so object is accelerating:
Transverse & Longitudinal Waves can be represented by sine waves. Longitudinal Waves can be graphed as density of particles vs time. Then will graph as sine wave.
Period (T) & Frequency (f) Period = time to complete one cycle of wave crests or troughs. Time for disturbance to travel 1. Usually measured in seconds. T = 0.5 s/cycle.
Frequency = Number of cycles in unit time. Inverse of period. Usually number per second called Hertz (Hz) Ex: 3 crests or cycles per second = 3s -1 or 3 hz
f = how often T = how long f = a rate T = a time T & f are inverse f = 1/Tor T = 1/f.
2. A wave has a period T of 5.0 seconds. What is its frequency? 0.2 hz
3. A wave has a frequency of 100 Hz. What is its period? 0.01 s.
4. The wave below shows a “snapshot” that lasted 4.0 seconds. What is the frequency of the wave? 4.0 seconds 2 cycles/4 s=0.5 Hz
Wave Speed Speed/Velocity = d/t If a crest (or any point on a wave) moves 20m in 5 sec,v = 20m/5s = 4 m/s.
Relationship of wave speed to wavelength( ) and frequency(f). v = d/tbut for waves d = 1 occurs in time T (1period) so v = /T since freqf =1/T v = f
5. A piano emits from 28 Hz to 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s. = 0.081 m to 12 m
Wave speed is constant if medium is uniform. Air at constant T and P. Homogenous solids. Water with constant T. Only the medium through which it travels! What determines wave speed?
7. A tuning fork produces a sound with f = 256 Hz and in air of 1.35 m. What is the speed of sound in air? What would be the wavelength of this tuning fork is sound travels through water at 1500 m/s? 346 m/s 5.86 m
Velocity depends on medium’s properties: -EM waves all travel at c in a vacuum. - EM waves slower through materials. -Vibrations travel faster on tighter strings - slower on loose strings. -v sound constant in air but depends on temp/density of air.
8. What determines the wave’s frequency? Vibrational Rate
Wave song http://www.youtube.com/watch?v=EzU79Egl3-c
Example Problems & Hwk. Read Text 12 - 3 Read Text Chap 12-3 Do pg 470 #23- 32, 35, 36. Write all out will collect.
Quiz 1. What is only factor that determines wave speed. 2. Give a real life example of: –A longitudinal wave –A transverse wave. Sketch a transverse wave. Label the –Wavelength –Amplitude –Equilibrium position
Reflection- a wave incident on a boundary (new material), part bounces off, part transmitted.
Example Echo: A sound wave is traveling in air at STP. The echo is heard 2.6 second later. How far away is the reflecting object? Time to object = 1.3 seconds. Speed sound STP = 331 m/s v = d/t tv = d (1.3s)(331 m/s) 430.3 m
How do multiple waves combine? Waves can overlap and occupy the same space at the same time. How they do it depends on the position or phase of the crests and troughs. Superposition – constructive destructive interference.
Phase of Particles in Wave “in phase” = points in identical position. Whole number of apart.(A,F B,G E,J C,H) 180 o out of phase = equal displacement fr equilibrium but moving opposite directions. Odd number of ½ apart. (A,D)
Superposition /Interference– 2 or more waves or pulses interact/superimpose & combine. Their amplitudes add or subtract. The resultant wave is the sum of the two.
Constructive Interference – waves superimpose with displacement in same direction + or -, amplitude increases.
Destructive Interference- waves or pulses meet with opposite displacement. Waves partially or totally cancel.
Points on waves that meet “in phase” interfere constructively.
Points that meet “out of phase” interfere destructively. Below is total destructive interference.
Standing Waves Wave pattern that results when 2 waves, of same f,, & v travel in opposite directions. Often formed from pulses reflected off a boundary. Waves interfere constructively & destructively at fixed points.
Standing Wave – wave appears to be standing still. No net transfer of energy.
Standing wave formed from wave pulses in same medium.
Nodes are points of max. destructive interference. Antinodes = points of max. constructive interference.