Digitized Sound

Human Hearing

Things that physically vibrate in air transfer some of that energy into the air in the form of sound waves. If the frequency of these waves is within our audiable range, and the level sufficiant, then we are able to hear these vibrations. To undersand sound, we must be able to measure it. Frequency is the number of back and forth movements that occur every second [cycles per seond], and is assigned the unit 'Hertz'. We hear a change in frequcncy as a change in pitch. Another characteristic of sound is intensity. Sound Intensity is measured as the RMS perpendicular energy through a unit area in unit time and has the unit of watts per square meter [W/m²]. Sound Intensity Level {SIL] is measured in decibels of Sound Intensity with 1 pW/m² as the reference. Sound Pressure is measured in N/m². Sound Pressure Level [SPL] is measured in decibels of Sound Pressure with 20 µN/m² as the reference. SIL and SPL are not the same except at a certain product of air density and speed of sound. At 20°C and atmospheric pressure at sea level [0.76 m Hg], SPL = SIL + 0.5. At 38°C and atmospheric pressure at sea level, SIL and SPL are essentially the same.

Many years ago, Dr. Fletcher and Mr. Munson were given the task of determining how our sensitivity to sound changed as a function of frequency and intensity. Using 1000 Hz as the reference, it was determined that a level of .0002 dynes/cm² [20 µN/m²] was the softest tone a person with good hearing could hear. This was defined as '0 db SPL'. The sound Pressure level [SPL] of other frequencies that had the same loudness were then measured and then plotted as the '0 db' loudness level. Next the SPL of the 1000 Hz reference tone was increased by 10 db, which is a tenfold increase in power, and the process repeated. This was done until the sound level became painful at about 120 db SPL. [The SPL shown here is valid at 38°C and atmospheric pressure at sea level.] The resulting loudness contours look like this:

What these curves tell us is that loudness of bass frequencies decreases much faster as SPL is decreased then for mid frequencies. Here is a wave file that may be played that contains tones at a level 20 db below maximum CD level for each of the following frequencies:

   1000.00 Hz   0.5 Sec
     20.00 Hz   0.5 Sec
     31.25 Hz   1.5 Sec
     46.88 Hz   0.5 Sec
     62.50 Hz   1.5 Sec
     93.75 Hz   0.5 Sec
    125.00 Hz   1.5 Sec
    187.50 Hz   0.5 Sec
    250.00 Hz   1.5 Sec
    375.00 Hz   0.5 Sec
    500.00 Hz   1.5 Sec
    750.00 Hz   0.5 Sec
   1000.00 Hz   1.5 Sec
   1500.00 Hz   0.5 Sec
   2000.00 Hz   1.5 Sec
   3000.00 Hz   0.5 Sec
   4000.00 Hz   1.5 Sec
   6000.00 Hz   0.5 Sec
   8000.00 Hz   1.5 Sec
  12000.00 Hz   0.5 Sec
  16000.00 Hz   1.5 Sec
  20000.00 Hz   0.5 Sec
   1000.00 Hz   0.5 Sec

Note that the following file if a very large multi-megabyte file and will take time to download.

Tones @ -20 dbfs

Most people will not be able to hear 20000 Hz unless they have exceptional hearing and their equipment is capable of reproducing a 20 kHz tone. Many will not be able to hear 16 kHz. Unless you have an exceptional system, you will probably not hear frequencies below 60 Hz.

The following file is a sweep from 22050 Hz. down to 20 Hz. Note that the following file if a very large multi-megabyte file and will take time to download.

Sweep @ -20 dbfs

While you play this file, listen for changes in amplitude caused by a non-even response in your playback system and your ears.

The human characteris of frequency is pitch. Higher frequencies have a higher pitch. It is interesting that pitch, our response to frequency, is logrithmic. Bach quantified our measurment of pitch when he developed the equal tempered scale. Since then, in Western music, the musical octave consists of 12 geometric steps. Note that the octave is named for the 8 whole notes it contains, but consists of 12 steps when all the notes are included, and is a factor of 2 in frequency. Thus each step is a frequency ratio of the twelveth root of two or about 1.059463094. On a guitar, if you divide the distance from a fret to the bridge by this number, you will have the distance from the next fret to the bridge. The length of pipes [top to mouth] in a pipe organ also follow this ratio. A rank of standard pitch will start with an 8 foot pipe [8']. A Rank with pitch an octave higher would be called a 4' rank. Divide the length [top to mouth] of a pipe by the twelveth root of two to get the length of the next pipe that is a semitone higher.

Scale @ -20 dbfs Scale steps from middle 'C' to 'C' an octabe above in half tone steps of 1 second each.

The next characteristic of sound is intensity. Intensity can physically measured as an RMS pressure in dynes per square centimeter or newtons per square meter. The human characteristic of intensity is loudness. Higher pressures sound louder. It is interesting that loudness, our response to intensity, is logrithmic. For this reason the metric 'bel' is used to represent a power ratio of 10. But 'bel' is too course a measurement, so tenths of a bel called decibels are used to measure sound pressure level. A decibel is therefore a power ratio of ten to tenth power, or about 1.258925412. 0 db SPL was selected to be .0002 dynes/cm² which, at a frequency of 1000 Hz, is near the threshold of hearing for those with good hearing. The chart above shows the relationship of loudness at 1000 Hz to loudness at other frequencies. The difference between the softest tone we can hear [0 db SPL] and a tone the is painfully loud [about 120 db SPL] is a power ratio of about ten to the twelveth power, or about 1000000000000:1. A very wide range indeed! Note that the chart also shows intesity in watts per square meter.

The third characteristic of sound is harmonic structure. Musical instruments do not make pure tones. Some instruments like a flute have few harmonics. Stringed instruments have a very complex harmonic structure. Brass instruments tend to emphasize one band of frequencies or another. It is the harmonic structure that allows us to identify the instrument that made the tone, or what vowel is being spoken. For an instrument that is blown or bowed, the harmonics are multiples of the fundamental frequency. i.e., for the pitch of middle 'A', the frequencies would be 440 Hz,, 880 Hz,, 1320 Hz,, 1760 Hz,, 2200 Hz., an etc. For instruments that are struck, such as a piano, drum or bell, the harmonics are real numbers [not integers]. For this reason, a piano to be played as a solo instrument, is tuned with the octaves stretched. [frequency ratio greater than two]

Sampled Sound

To get a digital representation of sound, it must be sampled and quantized. To do this, a microphone is used to convert the sound into a voltage. That voltage is amplified and then fed into an analog to digital converter. An example of such an analog to digital converter is Transit USB made by M-Audio. It connects between a laptop [or other computer with a USB port] and the amplified voltage representing the audio. This A/D converter can be set to sample the voltage on both cannels 44100 times a second at a precision of 16 bits. The computer takes this data and stores it on its hard disk. With a sample rate of 44100 Hz, it can accurately convert all input frequencies between 20 and 20,000 Hz. Normally the recording level is set so that the loudest RMS sound level is about 18 db below full scale of +/- 32767. This prevents the input signal from trying to exceed 32767 which would cause distortion. Trying to exceed the maximum value is refered to as 'clipping'. Since 16 bits represents a range of 20 log(32768) or 90 db, this gives signal to noise ratio of 72 db. With this digital representation in a computer, it can be digitally processed. This means edited for lenth, changing its level, using equalization to correct tonal balance, and adding effects such as reverberation. The modified file can then be saved to a CD in red book audio format that allows it to be played on any CD player. (Note that the Transit can sample both channels at the higher resolution of 24 bits and at a rate of 96000 Hz for higher fidelity.)

A CD player does the reverse of the recording process. The CD player takes the digital representation of the desired sound off the disc, uses a pair of Digital to Analog [D/A] converters to convert the samples into analog voltages that can then be amplified to drive a pair of loud speakers. The gain of the amplifier can be set so that the sound is recreated at the original level recorded, but more often the gain is set at a comfortable level.

Sampled sound is usually stored in wave format. For example sweepdownfast.wav is a wave file that quickly sweeps from 22050 Hz down to 20 Hz. A program that can be used to edit sampled sound in the wave format is Acoustica. It will allow you to cut and paste audio segments, and adjust level, balance and tonal quality. The saved wave files can then be transferred to an audio Compact Disc.

As famous as the Fletcher - Munson curves are, it should be noted that they were based on a sample of individuals with good hearing. When I was in college, a group of engineers did an informal test to see who could hear the highest frequency. A small speaker was connected to an oscillator and the person being tested stood about 20 feet from the speaker. Most of us could hear 18 kHz but not 20 kHz. But one engineering student could easily hear 23 kHz, a frequency beyond the capability of a red-book CD. As we age, the highest frequency we can hear decreases. I suspect that most males over 50 years of age would have trouble hearing anything above 14 kHz. This loss is due to the effectgs of aging and exposure to out noisy city environment. What is sad is the number of young adults that have lost their abiity to hear high frequencies becasue of exposure to high Sound Pressure Levels from headphones or ear buds connected to radios, CD players, i-pods, etc. If the person sitting next to you can hear music from the ear bud in your ear, you have damaged your hearing.

This Web Site was designed by Russ Lemon