Simple Harmonic Motion “things that go back and forth”

Our “Spring Chicken” follows a specific sequence to make one full oscillation –Down –Return –Up –Return When the chicken goes below “equilibrium,” (- x) that means the Force is pulling up (+F). Then Chicken goes above “equilibrium,” (+x) and Force is now pushing down (-F). The farther away it goes, the spring just pulls harder to bring it back in the same amount of time! The Thing about Springs...

SHM Any periodic motion that is the result of: –A restoring Force that is proportional to the –displacement of the object Is called Simple Harmonic Motion It is explained with “Hooke’s Law:”

Pendulum

crest trough - wavelength More waves in the same amount of time means higher frequency. As frequency increases, wavelength decreases! Medium oscillates perpendicular to energy’s direction Medium is a material that can vibrate with SHM

Longitudinal Waves Compression R a r e f a c t i o n wavelength Medium oscillates parallel to energy’s direction Period is the time for one wave, oscillation, revolution, swing, etc. to occur Units: sec Think =sec/vib Frequency is the number of vibrations that occur in one second Units: vib/sec Also known as : Hz

Frequency & period are inverses of each other The speed of a wave remains constant within a uniform “medium.” With a constant speed, frequency & wavelength are inversely related

Springs Pendulum Waves

Springs Hey, where’d that “2  ” come from?

Pendulums One other type of periodic motion is demonstrated by a pendulum

Springs & Motion What would happen if the “Spring Chicken” also moved left –to-right?

Wave Behavior Incident Wave: – the point when a wave crosses a medium boundary Reflected wave: –is the returning wave

Principle of superposotion Two or more waves combine to form a new wave –The result is called interference Destructive interference – Waves of opposite amplitude meet leading to a zero amplitude point before continuing unchanged Node = zero amplitude point constructive interference –Waves of same amplitude meet leading to greater amplitudes before continuing unchanged Antinode = higher amplitude point

Standing Waves in Strings When the whole string vibrates as one, then it can only fit a crest or a trough, not both. When the frequency is twice as much, the string can now fit one full wavelength. The next opportunity for a whole crest to fit is when there are 2 crests & a trough

Definitions: –Node: Points of destructive interference No displacement –Antinode: Points of constructive interference Maximum displacement –Fundamental: basic frequency of a material n=1 –Harmonic: multiples of the fundamental (higher octaves) Standing Waves in Strings

Frequency Equations Take all of our general equations for wavelength, and substitute in v/f Strings (2 fixed ends) n = 1, 2, 3 …

If we translate the compressions & rarefactions to crests & troughs, we see this: At the fundamental wavelength, one quarter of a wave can fit in the tube at a time. By simply hitting one end of a tube, a compression of air travels the length of the tube. Standing Waves in a Tube One End Closed At the end of the tube, no air can vibrate- it must be a node. The following harmonic must be 5/4 of a wave. What is the pattern here? Every harmonic wavelength must end with a node, so the next harmonic must be ¾ of a wave.

Standing Waves in a Tube Both Ends Open Air can vibrate at both ends of the tube- not a node at the end That means that the fundamental is one half of a wave Each harmonic must then be a multiple of one-half of a wavelength

Frequency Equations Take all of our general equations for wavelength, and substitute in v/f These are your standing wave equations! Really, there are only two equations to remember… Strings (2 fixed ends) Tubes (1 open end) n = 1, 2, 3 … n = 1, 3, 5 … Tubes (2 open ends) n = 1, 2, 3 …