Less than 10 Hz - hear an average pitch of 1/2(f₁ + f₂) and beats.

Greater than 15 Hz - Critical bandwidths overlapping. Hear one tone but dissonant. 30-40 Hz the worst.

Greater than half step - hear two distinct tones, but still dissonant.

Greater than Critical Bandwith - hear two distinct and consonant tones. Also a difference tone.

Consonance/Dissonance -if beats occur in the range of 10 - 50 Hz for the fundamental or any harmonics, the two notes sound dissonant.

Role of medium - Doppler shift occurs when there is motion with respect to the medium.

Moving observer - a moving observer will detect a shifted frequency given by:

*

.

Moving source - a moving source will produce a shifted frequency given by:

*

.

Double Doppler Shift - If both source and observer are moving, first find the Doppler shifted frequency for an observer at rest in the medium. Then this observer bcomes a stationary source for the next part.

Reflection - a reflected wave acts like it is produced by the reflecting surface.

Sonic boom - source traveling faster than the speed of sound.

Cherenkov radiation - source traveling faster than the speed of light.

Wake of a boat - source traveling faster than the speed of water waves.

Mach Cone - the shock wave forms a cone. The angle of the cone is given by

*sin(q) = v_wave/v_source

Gain - increase in the amplitude of a wave due to amplification.

Overall gain - overall increase or decrease in a wave due to amplification or loss.

Feedback - occurs when a loop exists between the source of a wave and the detection of a wave and the overall gain exceeds one.

Cavity feedback - occurs at resonant frequencies of a cavity for which the overall gain exceeds one.

A plot of the resonant frequencies of a cavity as a function of some variable that is being changed.

Medium - not well understood.

Speed - speed of light = c = 3× 10⁸ meter/second.

Doppler shift at low speeds - just like other waves.

Steps - reflection off of steps produces a tone. Can get constructive and destructive interference.

Thin films - reflection off of thin films can lead to constructive or destructive interference.

Parts of the ear - ear canal, ear drum, small bones, oval window, cochlea.

Critical bandwidth - range of frequencies that respond to a given pitch. The CB is equal to 19% of the frequency unless the frequency is 500 Hz. Below 500 Hz the CB is always 90-95 Hz.

Just noticeable difference - smallest interval that can be heard. The JND is equal to 0.5% of the frequency.

Pure tones - contain no overtones.

Complex tones - contain some amount of overtones, gives tone quality or timbre.

Consonance/dissonance of complex tones - must compare the overtones with each other.

"Missing fundamental" - pitch of a complex tone given by the fundamental frequency, even if that frequency is not present in the tone.