Simple Harmonic Motion. 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.
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Simple harmonic motion (SHM) refers an oscillatory, or wave-like motion that describes the behavior of many physical phenomena:
Objects undergoing SHM trace out sine waves where the d is pos and neg with time.
Can waves do work?
Gasses - air
Solids - wood
Ex: Sound/Earthquake waves
Particles vibrate perpendicular to energy transport. Trace out sine wave.
in air molecules from vibrating tuning fork or vibrating string.
Longitudinal Waves can be graphed as density of particles vs time. Then will graph as sine wave.
Period = time to complete one cycle of wave crests or troughs. Time for disturbance to travel 1l.
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
2 cycles/4 s = 0.5 Hz
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(l) and frequency(f).v = d/t but for waves d = 1l occurs in time T (1period)so v = l/Tsince freq f =1/Tv =lf
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.
l = 0.081 m to 12 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.
Reflection- a wave incident on a boundary (new material), part bounces off, part transmitted.
Pulse Passing into new medium from less dense material. What happens to pulse?
The resultant wave is the sum of the two.
– waves superimpose with displacement in same direction + or -, amplitude increases.
Hwk Text pg 471 #33 - 44, 48-49
Standing WavesWave 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.
Nodes are points of max. destructive interference.Antinodes = points of max. constructive interference.
n ( ½ l) = L
n is a whole number