Last chapter we learned that sound is caused by a disturbance in the equilibrium of air particles. Now let's look closer at the sound waves themselves.

A sound wave emanates from the cause of the disturbance. It is comprised of colliding particles that transfer energy as they bump each other until the energy is split so much that it dissipates. A receptor, such as an ear or microphone diaphragm, placed in the path of the sound waves reacts to the varying pressures that the wave presents. Both the ear and diaphragm turn the varying pressures into electrical energy that our brain can interpret as sound.

These pressure changes can be produced either periodically or aperiodically.

Periodic is a constant fixed vibration, such as a piano hammer hitting the string inside the piano. The string vibrates at a constant fixed rate. The air around the string moves back and forth at the same fixed rate creating a fixed pitch. (Go back to our pond, if you wiggle your hand in the water at a constant rate, you are causing periodic pressures, or vibrations.).

An  aperiodic event on the other hand, is  random non-pitched event such as an explosion, hand clap, or a cymbal crash. There isn't a fixed rate of vibration in a periodic event. Just one event that causes a disturbance.( Back to our pond, slap the water with your hand and you will cause an aperiodic event.).

(A simple way to remember these terms is that aperiod is a single period. While periodic is multiple periods. )

In a musical sense, periodic vibrations are more interesting since melody and harmony are all comprised of periodic events. So we are going to focus on periodic events.

Vibration physics; a. Rapid motion of a particle or of an elastic solid about an equilibrium position b. Any periodic process.

Go back to the piano. If it is a grand piano, open the lid and look at the strings inside. Notice that from left to right, the strings get shorter, as well as thinner. Strike the key all the way to the left, then strike the top key. Which string vibrates faster? Which slower? How does the pitch of the various strings relate to the vibrations?

OK..back to the pond. If you drop a bowling ball into the pond, and then after the pond is still again, drop a golf ball in, which ball created larger waves? How would the pitch of the sound of the different balls differ as they hit the water? Which wave traveled the farther distance? Which waves where closer together?

Let's dissect the wave. Pluck a string of a guitar and it vibrates. The thicker strings vibrate slower and have a deeper pitch than the thinner strings. One vibration of the plucked string is a cycle. Like a pendulum, the string bends one way as you pick it, and then bounces back twice the distance the other direction . That is one cycle. The furthermost distance the string travels in either direction from the center, is the antinode (area of maximum displacement +/-), and the calm state that it was in before being picked is the node (area of minimum displacement).

The highest pressure is the + antinode, and the lowest pressure is the - antinode.

Watch a speaker pumping a bass note and you will see the positive peak amplitude and negative peak amplitude and pressure.

The time it takes to complete one cycle is one period.

Frequency

The number of cycles that take place in one second is the frequency of thesound wave. Frequency is measured in hertz (Hz). In other words, concert pitch is considered to be A-440 Hz, which means 440 cycles per second - which is the pitch A. The Hz of a sound wave corresponds to the pitch that you hear. The lower the Hz (cycles per second), the lower the pitch and visa versa. You will see many things measured in Hz. Including video, color, light, electricity, computer speed, and more.

Kilohertz (kHz) is an abbreviated form of hertz x 1000.

Megahertz (mHz) is an abbreviated form of Hz x 1,000,000.

The human hearing range is 20 Hz - 20 kHz. Which means that we can hear sound that is between 20 cycles per second...to 20,000 cycles per second.

Cats can hear up to 60,000 Hz. Bats use 50 kHz echoes for a guidance system. They bounce cries off of objects at a rate of 50 cries per second.

The average human anal sphincter resonates at about 77 Hz. Police have experimented in the control of mobs by employing loud sounds at this frequency.

( Actually , we must remember that as we get older, our ears lose the ability to respond to high frequency sounds. At an advanced age we could have a response that extends up to 6 kHz. If you insist on pumping the volume level of your music you may also cause damage to your ears and lose hearing response much sooner.)

Dogs can hear above 20 kHz. That is why a dog can hear a dog whistle and we can't. Radio waves are again, out of our perception range. Even cosmic rays can be measured at 10 to the 22nd power Hz....way above our hearing range. Most digital audio devices are designed to respond to our hearing range of 20 Hz to 20 kHz. The assumption being that there is no reason to record for playback what we can't  hear. (That assumption is being challenged with the thought that frequencies we don't consciously detect, are still registered by our brain and contribute to the overall sound or feeling of what we hear.)

Frequencies above 20,000 Hz are considered to be ultrasonic. Below 2,000 - infrasonic.

Frequency Table of Musical Notes. 

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• Human hearing range is 20Hz-20kHz (20,000 Hz)
• Each value represents one octave. For example, A-880 is 1 octave higher than A- 440. A-220 is one octave lower.

An example of pitch to frequency relationship , is your car. If you accelerate your engine, the pitch goes up. Why? You have increased the rotations per minute of the engine.

Frequency response

This leads us to frequency response , the way something responds to given frequencies. You may find that a monitor speaker has a frequency response of 70 Hz - 18 kHz while a microphone from 20 Hz - 20 kHz. While the microphone 'hears' 20 Hz , the speaker does not respond to the frequency.

(Examples: Alesis Monitor One speakers respond from 45 Hz -18 kHz. An AKG 414 B/TL II mike (vintage) ranges between 20 Hz and 20 kHz.)

Notes played on a piano have frequencies between 27.5 Hz and 4 kHz. The frequency response of human hearing we have learned is between 20 Hz and 20 kHz , but there is a breakdown in precision and consistency of pitch judgments above 4 kHz, the highest pitch of the piano.

The ear is most sensitive to frequencies between 2kHz and 5.5 kHz, which is also the region of human speech sounds.

The ear has extra sensitivity in the 2 kHz and 4 kHz range, interestingly the range of both male and female screams. Consonants - t, p, k, b -normally are at 4 kHz. Speech falls in the 3 kHz to 8 kHz range.

Pitch.

Note the difference between frequency and pitch is that frequency is a measure of the rate of disturbance, while pitch is what our brain does with the data it receives. A 'tone deaf' person has a malfunction (for lack of better word) in either the ear mechanism or the brain's interpretation of different frequencies.

Pitch is closely related to frequency, as seen in the keys of a piano . The ratio of frequencies between two keys is constant (around 1.06). Therefore , the logarithmic scale for frequency matches up with the constantly spaced keys.

We also see this relationship in music notation as notes move up with frequency. 

1. give examples of periodic and aperiodic events.

2. Find the frequency response for different items (reverbs, tape decks, video gear, computer chips, etc.). Look in manuals or literature.

3. Memorize the complete frequency table . (Just KIDDING!)

4. Show or discuss examples of pitch to frequency response. (For instance..different tuning forks)

5. Be ready to calculate frequencies an octave up or down.