A pitch sensation often occurs in free nature when the sound of a sound source reaches the ear of an observer directly and, at the same time, after being reflected against a sound-reflecting surface. This phenomenon has been named Repetition Pitch (RP), because the addition of a true repetition of the original sound to itself is the basic requirement (Bilsen, 1966). RP corresponds to the reciprocal value of the time delay between the original and the repeated (reflected, delayed) sound. RP is most salient when the original sound is wide band and pitch-less itself (for example: white noise). Probably the first written report of the phenomenon dates from Christian Huygens (1693), who observed such a pitch in the sound from a fountain reflected against the steps of a large stone staircase in the garden of the castle of Chantilly in France (see Oeuvres Complètes, Vol.10, Correspondance no.2840, pages 570-571, see Gallica; see DBNL, see also RPnature). A similar example stems from the Mayan step pyramid in Chichen Itza (see ocasa; for a detailed explanation see  RPglide). In free field, one might also be able to observe a gliding pitch when a plane flies over, by moving one's head towards and from the ground. Or more nostalgic, when one approaches a steam locomotive blowing off steam. In music, the phenomenon is sometimes deliberately created by electronic means (delay and add) to superimpose a pitch or coloration effect on the original music (see Flanging). In room acoustics and sound recording, the phenomenon often causes an unwanted coloration of the original sound. Blind peoples might use RP to locate obstacles by clicking the street surface with their cane, thus producing a wide-band impulsive sound that is reflected by an obstacle. Numerous experiments in the past, in the field of psychological and physiological acoustics, aimed at understanding the perceptual and neurological processes underlying pitch perception in general, RP in particular. Both temporal and spectral models of pitch extraction were proposed (RP-prediction; see also References).

     Pictures drawn by F.M.M, Bilsen 

Sound examples:

• RP+ Two-octave scale in repetition pitch from digital noise delayed and added to itself, stretching from G2 (10.20 ms delay) to G4 (2.55 ms delay),
• RPm Two-octave scale from noise with many mutually-equal-distant repetitions added (named IRN by Yost, 1996), thus producing an intensified RP,
• Locanimat A digital animation with intensified RP illustrating the perception of pitch or coloration due to a single sound reflection from the ground,
• Locomovie Fragment taken from an arbitrary movie showing a steam locomotive passing by and producing a changing RP sound at a (fixed) microphone,
• Chantilly Video of handclapping at the staircase of the castle Chantilly. Note a rather salient RP due to mutually-equal-distant reflections (compare IRN),
• Chichen Itza Three sounds in sequence: a handclap, the pyramid's response (from ocasa), and a synthesized RP glide following the pyramid's dimensions.
  

Three key publications:

• Bilsen, F. A., and Ritsma, R. J. (1967/68). “Repetition pitch mediated by temporal fine structure at dominant spectral regions,” Acustica 19, 114-115. PDF
• Bilsen, F. A. (1977). “Pitch of noise signals: evidence for a ‘central spectrum’,” J. Acoust. Soc. Am. 61, 150-161.
• Sayles, M., and Winter, I.M. (2007). “The temporal representation of the delay of dynamic iterated rippled noise with positive and negative gain by single units in the ventral cochlear nucleus,” Brain Res. 2007.06.098

A dichotic or binaural pitch may be observed when continuous white noise is presented by headphones to the left and right ear of a listener. Given a particular interaural phase relationship between the left and right ear signals, a sensation of pitch occurs. In other words, stimulation of either ear alone gives rise to the sensation of white noise only, but stimulation of both ears together produces the pitch. Generally, a dichotic pitch is perceived somewhere in the head amidst or separate from the background noise. To be more specific, the dichotic pitch is characterized by three perceptual properties: pitch value, timbre, and in-head position (lateralization) of the pitch image. The first binaural pitch phenomenon reported in the literature is the so-called Huggins Pitch (HP) (Cramer and Huggins, 1958). In this case, the interaural phase relationship consists of a rather sharp phase shift over 2 pi radians in a narrow-band frequency region of the white-noise spectrum. The sensation is of a fluctuating pure tone. Probably the strongest dichotic pitch ever is created by having several harmonically-related phase-shift regions. It is therefore called multiple-phase-shift pitch (MPSP, Bilsen, 1976; see also sirl for a similar stimulus). Experiments on dichotic pitch were motivated by the study of pitch in general and of the binaural system, being crucial for sound localization and separation of sound sources (see cocktail party effect). Various models were developed in the past. Especially, the so-called CAP-CS model  seems successful in predicting both the pitch value and pitch-image position (see References).

One of the problems with conventional hearing aids is malfunctioning in situations with disturbing background noise like, for example, in a cocktail-party or meeting-like situation. Therefore, around 1983, I proposed a project at the Delft University of Technology aiming at a new type of hearing aid that would enable hard-of-hearing peoples to focus on a particular voice amidst of other disturbing voices and/or noises. In general, three strategies seem feasible: 1) the use of two identical conventional hearing aids, provided that both ears have degraded about equally, 2) the use of a conventional hearing aid supplied with binaural-like signal processing, and 3) the use of one or two conventional hearing aids with a strong directional microphone. Given the knowledge and experience available in the TUD Sound Control Group, the latter option was chosen and this has resulted in the "hoorbril", a pair of spectacles with an array of microphones mounted either on the legs (endfire array) or on the body itself above the glasses (broadside array). Financial support was supplied by the Dutch Organization for Scientific Research (NWO) and the Philips Company. Today, the company Varibel produces and sells an hoorbril based on the endfire principle. See also Babble for similar products.

Specific publications:

• Bilsen, F.A., Soede, W., and Berkhout, A.J. (1993). “Development and assessment of two fixed-array microphones for use with hearing aids,” J. Rehab. Res. Developm. 30, 73-81.
• Soede, W., Berkhout, A.J., and Bilsen, F.A. (1993). “Development of a directional hearing instrument based on array technology,” J. Acoust. Soc. Am. 94, 785-798.
• Soede, W., Bilsen, F.A., and Berkhout, A.J. (1993). “Assessment of a directional microphone array for hearing-impaired listeners,” J. Acoust. Soc. Am. 94, 799-808.

Basics summarized
In classical mechanics, the movement of rigid bodies is generally described by two analogous vector equations: F = dp/dt for translation of the center of mass, and M = dL/dt for rotation around the center of mass, with F the total external force, p the momentum (dutch: impuls), M the moment of forces (koppel of krachtmoment), and L the angular momentum (impulsmoment).

TippeTop explained
As an example, we consider the intriguing movement of the so-called tippe top or Kelvin top after its inventor Lord Kelvin (Sir William Thomson). Such a top essentially consists of a spherical body and a cylindrical stem, with the center of mass displaced from the center of the sphere. After having been put into rotation around its axis of symmetry vertically, the top gradually changes its movement and eventually it flips over into a stable rotation on and around the stem. We have to conclude that the rotation has changed sign, such that the angular momentum vector L still has its original vertical position. Further, the center of gravity has moved upwards, apparently at the cost of a decrease in magnitude of L. This unexpected behavior is explained by the action of a small friction force at the contact point of the top with the ground surface. Many publications in the past have been devoted to the explanation of the complex movement of the tippe top. Here we propose a qualitative explanation using the above equations only. For further details and demonstrations see TippeTop1 and TippeTop2

Spinner showing precession
This recent hype flywheel thing can also learn us a lot about classical mechanics movie A Spinner is mounted on a pencil suspended by a rope. It is started rotating firmly. Its angular momentum L is directed horizontally along the pencil. A moment M due to the gravital force works perpendicular on L. It can only change the direction of L, not its magnitude. The resulting rotation of L in a horizontal plane is called precession.