Aspects of Sound
We have mostly completed our introduction to the basic physics necessary for an understanding of sound. Believe it or not, our task now gets more complicated, as we shift our focus from a mere quantitative analysis of sound to the more difficult area of how living things perceive sound. Even though perception is an area of study that lies outside of physics, great strides have been made in the past ~100 years in relating perception to simple physical processes. There continues to be hope that all perception can be understood from the underlying physical processes that take place in our sensory organs and our brain.
By necessity, perception, and of direct relevance to this course, the perception of sound, involves subjective aspects which are qualitative in nature: pleasing sounds are defined as such by individuals, there is not universal agreement about what sounds good! Because of this, our emphasis will remain on relating qualities of sound to things which we can measure (i.e., quantities). A correspondence between a sound quality and the dominant measureable quantity is presented below in a table.
| Sound quality | Measurable quantity
|
|---|
| loudness | amplitude of pressure oscillation
|
| pitch | frequency of sound waves
|
| timbre | pressure oscillation waveform
|
| duration | time interval
|
| direction | energy-flow
|
We'll be talking about each of the measurable quantities in greater detail in the coming weeks. Today, we simply start with an introduction to these quantities and begin showing how they are related to subjective descriptions of sound.
Duration
This is probably the quality that is simplest to relate to a measureable quantity: the duration of a sound is the time interval between its beginning and end points. Our hearing system is capable of detecting and distinguishing a very short sound, even if it contains only a few cycles of air pressure oscillation. We can distinguish between different types of short sounds: a click is distinguished from a pop. If such sounds are repeated often enough, we lose the ability to distinguish individual pops and clicks. Instead, we perceive a hum. Repeat frequencies of 20-30 Hz is generally where the perception changes. This is completely analogous to our perception of motion in movies, which are nothing more than different still images that are changed at sufficiently large frequency. When the frame rate of still images is large enough, our brain loses its ability to distinguish the individual still scenes. Instead, it perceives motion.
Direction
Our brain combines information from our two ears to perceive the direction to the sound source. At frequencies higher than ~1,700 Hz, the wavelength of sound waves is smaller than the distance between our two ears. This allows intensity differences at our two ears to be used for localization of the source. At frequencies lower than ~1,700 Hz, the intensity differences at our two ears are too small to be used for determination of the source direction. Instead, tests of hearing reveal that our brain uses the very small arrival time difference of sound waves at each ear to deduce the direction to the sound source.
Loudness
Another attribute of sound that is easily quantified is loudness. It is related to the amplitude of the pressure oscillation in a sound wave. Our perception extends over such a broad range of amplitudes (with the perceptible limits depending on frequency) that we use a logarithmic scale.
We will be distinguishing sound pressure levels which are directly related to the amplitude of sound waves, from sound power levels, corresponding to the rate of energy transfer with time, and sound intensity levels.
Pitch
The qualitative perception of pitch is closely related to the measurable frequency of a periodic pressure oscillation associated with sound waves. These periodic oscillations, in general, have some level of contributions from all frequencies of the harmonic series:
f, 2f, 3f, ...
The pitch of a sound is generally associated with the fundamental in the harmonic series, and the timbre of sound, by how much amplitude is given to the higher harmonics that are superimposed (or added) to the fundamental.
Humans can perceive sounds in the frequency range 20 Hz < f < 20,000 Hz (or 20 kHz). There are variations in the perceptible frequency range amongst individuals and also variations with the age of an individual (hearing loss generally occurs first for high frequency sounds). The factor of 1,000 in the range of frequency (the ratio of the maximum to minimum perceptible frequency) is approximately 10 musical ocatves. An octave separation of two tones corresponds to a factor of two difference in their frequencies. Hence, two tones separated by 10 octaves have frequencies that are different by two raised to the 10th power.
The variation in wavelengths corresponding to the audible frequency range can be found from
The variation in wavelengths corresponding to audible frequencies is 17 m at f = 20 Hz to 17 mm for f = 20 kHz. The high frequency end of perceptible sounds produce wavelengths comparable to the physical size of our ears.
Frequency perception is not linear. The difference between sound waves at with frequencies, f = 200 and 400 Hz is perceived to be smaller than for two tones at 400 and 600 Hz. Doubling of frequency produces pitches that sound similar. For that reason, musical scales are designed in octaves: two notes an octave apart differ from each other by a factor of two in frequency. The eight A notes on a piano span 8 octaves and correspond to frequencies 27.5 (A0), 55 (A1), 110 (A2), 220 (A3), 440 (A4), 880 (A5), 1,760 (A6) and 3,520 (A7) Hz. The labels in parentheses are used by Rossing to refer to musical notes.
Timbre
This is a more elusive qualitative attribute of sound. Quantitatively, it is related to waves with different shapes. Below, we show the pressure oscillations at a fixed position for two different waveforms having the same
frequency. The top graph shows a sound corresponding to a pure tone, this is a sound with the frequency of the fundamental in the harmonic series. The bottom graph has the same pitch, but sounds different because it is made by superimposing with the fundamental other harmonics. Quantitatively, we'll show how a Fourier analysis of the pressure oscillations with time can be performed to establish the amplitude of higher harmonics that contribute to different sounds.
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Last updated: 17 Oct 1999
Comments: bland@indiana.edu