Sound waves travel in air through the compression and rarefaction of air molecules. This compression and rarefaction happens in the same direction the sound travels. Therefore, sound propagates in air as a longitudinal wave.
However, sound propagates through solids in a different manner. In a string, for example, the vibration propagates as a transverse wave.
The speed of sound depends on the properties of the material through which the wave is traveling. Differences of temperature or air pressure can affect the speed of sound in air. In dry air at 20 °C the speed of sound is 343.2 m/s.
Amplitude represents the intensity of the sound wave and is related to the volume of the sound (though it is not exactly a direct relation). If the average square of the amplitude of a sound wave increases, the volume perception will also increase. In fact, the energy of a signal can be calculated using its’ amplitude.
Brief and drastic changes in amplitude might not cause a big change in volume perception, but they do cause an audible click. This sudden change in amplitude is known as pulse.
The frequency of a sound wave traveling in air is the number of cycles of compression/rarefaction per second, and is measure in Hertz (Hz).
Although in real condition there are always multiple different frequencies traveling together in a sound wave, there is a fundamental frequency, which is usually the lower frequency of that sound wave, and it’s related to the perceived pitch. Basically, the higher the fundamental frequency is, the higher the perceived pitch.
The perceived timbre of a sound wave depends on multiple factors, and probably the most important of them is the distribution of the harmonic partials of the wave. The harmonic partials are basically frequencies that are integer multiples of the fundamental frequency of the sound wave. The image bellow shows the harmonic partials of a vibration propagating in a string.
The timbre will be different according to the distribution of intensities between the harmonic partials of a sound wave. The image bellow shows the difference in the distribution of the harmonic partials for two different music instruments: a guitar and an alto saxophone.