Things You Need to Know
- Oscillatory Motion refers to a "back and forth" repeating motion.
- Simple Harmonic Motion is a type of oscillatory motion where the restoring force is directly proportional to the displacement from equilibrium position and acts opposite in direction to that displacement. A swinging pendulum is a classic example of Simple Harmonic Motion.
- In Simple Harmonic Motion:
- The maximum velocity (and thus the maximum kinetic energy) occurs as the object passes through equilibrium position.
- The maximum acceleration (and thus the maximum contained force) occurs at the point of maximum displacement.
- Transverse waves vibrate perpendicular to the motion of the wave.
- Ex: water waves, electromagnetic waves, etc.
- Longitudinal waves vibrate parallel to the motion of the wave.
- Ex: sound waves, seismic waves, etc.
- Diffraction occurs when a wave passes through an opening. In order for diffraction to occur, the width of the opening must be the same size or slightly smaller than the wavelength of the wave.
- Interference refers to when the amplitude of one wave affects the amplitude of another wave.
- Constructive interference is when two positive amplitudes create a larger amplitude.
- Destructive interference is when one positive amplitude and one negative amplitude partially or completely neutralize each other.
- Resonance is the vibration that occurs in an object when it experiences a periodic force with the same frequency as the object's natural frequency.
- The fundamental frequency (also called the 1st harmonic) is the lowest resonant frequency possible.
- Standing waves are waves that appear to just "bounce" up and down due to having points called "nodes" that don't appear to move.
- Anti-nodes are the points on a standing wave that move the greatest amount to create the amplitude of the wave.
- There are three situations we analyze in regards to harmonics:
- Fixed-end situations have nodes at each end when resonating, like in string instruments.
- Open-end situations have two open airs, which form anti-nodes when resonating. A flute is an example of an open-end instrument.
- Closed-end situations have one open end (anti-node) and one closed end (node) when resonating. A clarinet is an example of a closed-end instrument.
- Closed-end situations only resonate in odd-numbered harmonics.
- For fixed and open-end instruments, the frequency of the nth harmonic can be found using the formula: f = (nv)/(2L), where v is the speed of the wave and L is the length of the string/air column.
- For closed-end instruments, the frequency of the nth harmonic can be found using the formula f = (nv)/(4L).
Homework Assignment
Oscillatory Motion Homework | |
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