Waves

Position as function of time in SHM.

Velocity as function of time in SHM.

Acceleration proportional and opposite to displacement.

Maximum speed occurs at equilibrium position.

Period of mass-spring system.

Period of simple pendulum (small angles).

Total mechanical energy in SHM is constant.

Period of a rigid body oscillating about a pivot point (physical/compound pendulum).

Period of a torsional pendulum (object rotating about a wire or rod).

Displacement of a damped harmonic oscillator (underdamped case).

Measure of how underdamped an oscillator is; higher Q means less energy loss per cycle.

Maximum amplitude occurs when driving frequency equals natural frequency (resonance).

Fundamental wave relationship.

Period is inverse of frequency.

Angular frequency in radians per second.

Spatial frequency of wave.

Energy transmitted per unit area per unit time.

Intensity proportional to amplitude squared.

Intensity from point source decreases as 1/r².

Speed of transverse wave on stretched string.

Fraction of wave power reflected at boundary between two media.

Fraction of wave power transmitted through boundary between two media.

Velocity at which the envelope of a wave packet propagates; represents energy transfer speed.

Velocity at which the phase of a wave propagates through space.

Speed of sound depends on temperature and gas properties.

Logarithmic scale for sound intensity.

Frequency of amplitude modulation from two close frequencies.

Ratio of object speed to speed of sound. M > 1 is supersonic.

Half-angle of the Mach cone (shock wave) produced by supersonic object.

How to add multiple sound sources in decibels (cannot simply add dB values).

Frequency shift for moving source and/or observer.

Frequency increases when source and observer approach.

Frequency decreases when source and observer recede.

Approximate Doppler shift for electromagnetic waves when v << c.

Resonant frequencies for string fixed at both ends.

Resonant frequencies for pipe open at both ends.

Resonant frequencies for pipe closed at one end.