Pitch
Pitch is how high or low a sound seems to a listener; it is determined mainly by the frequency of the sound wave.
Definition
Pitch is how high or low a sound is: a whistle has a high pitch and a tuba has a low pitch, and it is separate from loudness, since a high note can be played softly and a low note loudly. It is the perceived highness or lowness of a sound, determined primarily by frequency, with higher frequency meaning higher pitch, and shorter, tighter, or thinner strings and shorter air columns vibrate faster and produce higher pitches, which is why small animals make high-pitched sounds and large ones make low-pitched sounds. Pitch maps mainly to fundamental frequency, but the mapping is roughly logarithmic, so equal pitch intervals correspond to equal frequency ratios, a semitone in equal temperament being a ratio of $2^{1/12} \approx 1.0595$; the pitch of a complex tone is generally that of its fundamental even when the fundamental is physically absent, because the auditory system infers it from harmonic spacing, and standing-wave physics sets the fundamental as $f_1 = v/2L$ for a string or open pipe and $f_1 = v/4L$ for a pipe closed at one end.
Example
On a piano, keys to the right make high-pitched notes and keys to the left make low-pitched notes because the strings on the left are longer and thicker and vibrate more slowly; concert A is $440\ \text{Hz}$, the A one octave higher is $880\ \text{Hz}$, and the A one octave lower is $220\ \text{Hz}$, since each octave up doubles the frequency. A pipe open at both ends and $0.5\ \text{m}$ long has $f_1 = 343/(2 \times 0.5) = 343\ \text{Hz}$ with harmonics at $686$, $1029\ \text{Hz}$, and beyond, while closing one end drops the fundamental to $343/(4 \times 0.5) = 171.5\ \text{Hz}$ and leaves only odd harmonics, which is why a clarinet sounds an octave lower than a flute of similar length.
Key Insight
A mouse squeaks and an elephant rumbles, partly below what humans can hear, because small vibrating parts oscillate faster than large ones. The Doppler shift is a change in pitch without any change at the source: the siren does not change, but the spacing of compressions arriving at the ear does, so pitch is ultimately about the frequency received, not the frequency sent.