The Wikipedia history of the choice of 44.1 kHz.
A more detailed explanation of MIDI.
A MIDI file. You can download this, open it with Audacity and compare the file with a regular mp3. It will also open with GarageBand and other software.

18c: Amplification

In the diagram on the left, below, we can imagine a small flow of water (labeled Signal) controlling a larger flow of water. This is the general idea of electronic amplification; a large current flow is controlled by a small current or voltage signal. Originally this was done using a vacuum tube. As shown in the second figure below, the tube has a positive end (anode) and a negative end (cathode) and all air has been removed. A large voltage is applied from anode to cathode so that electrons will stream from the cathode to the anode (just to be clear, recall that conventional current, I in Amperes that we talked about in the last chapter is labeled to flow in the direction opposite to the electron flow). A wire grill called the grid is placed in between the anode and cathode. If the grid is neutral, the electron flow from cathode to anode passes through the grid and a steady, direct current is produced. If a small signal is applied to the grid it affects the much larger current flow between anode and cathode. So for example, a low voltage sine wave applied to the grid becomes a large current sine wave flowing through the tube. The ratio of the output signal to the input signal is called the gain. This can be measured as voltage gain (ratio of voltage out to voltage in) or current gain (ratio of current out to current in).

Although they take much more energy to run than modern solid state amplifying circuits, tube amplifiers are still used by the military for radar and high power radio transmission. Some audiophiles claim that tube amplifiers produce a better sound than solid state amplifiers. A disadvantage of tube amplifiers is the tubes take up a lot of space, are heavy, use much more energy than transistors and will stop working if the vacuum seal breaks.

Transistors were developed in the 1940s and gradually replaced most vacuum tubes in electronic applications. Transistors work basically the same way as a vacuum tube. Two crystals (made of silicon or germanium) with slightly different electrical properties are put together separated by a third crystal as shown in the figure on the right, above. The emitter end of the transistor is made so that it has electrons ready to flow and the collector end will accept these electrons. When a voltage is applied across the transistor a current flows through the transistor and electrons flow from emitter to collector. The function of the grid in a tube is performed by a crystal called the base which has slightly different electrical properties from the emitter or collector. When a small signal is applied across the base, the larger current flowing from emitter to collector is controlled to have the same variations as the signal. The terms emitter, collector and base are replaced by source, drain and gate for some other types of transistors using different crystals with different electrical properties.

Transistor amplifiers take much less energy to run than tube amplifiers and generally can take much more physical abuse (shock, temperature changes, etc.) and still work. In theory a transistor should last forever because it is a solid crystal although some transistors can be destroyed by electrostatic sparks. They can also be made incredibly small (today's computer chips contain billions (10⁹) of transistors), making cell phones, mp3 players and other small electronic devices possible.

In addition to being used as amplifiers, transistor (and tubes) can also be used as electronic switches. In this application, the signal to the base either allows current to flow from emitter to collector or turns the current completely off. Transistors that function this way can be used to represent ones (all the way on) or zeros (all the way off) in a digital computer.

All amplification suffers from distortion. A perfect recording and playback process would exactly reproduce the original sound but this is never possible; there are always some unwanted modifications to the sound. Microphones, recording devices, speakers and amplification systems all produce some distortion of the signal. The difference between noise and distortion is that noise is extra, unwanted signals whereas distortion is the unwanted modification of the signal.

One form of distortion is when the voltage output is already at the maximum possible for the circuit and the signal amplitude increases. The result is the peaks of the output signal are cut off as shown in the diagram below. The original signal is the blue curve but the amplifier has a maximum output of 0.6 V so it clips off any part of the signal above 0.6 V (the red curve). The amplified signal will not sound right because the volume doesn't increase the way it was suppose to in the original recording. This is called amplitude distortion.

When there is amplitude distortion the effect of flattening the top of the output wave when it reaches the speaker is to introduce unwanted overtones. We know from Fourier analysis (Chapter 9) that the sudden change from a smooth curve to a flat top requires many extra harmonics to describe the new wave. These new harmonics change the sound produced by the amplifier/speaker system. This type of distortion is called harmonic distortion. Harmonic distortion also occurs if different frequency ranges are amplified by different amounts (in any part of the recording to playback sequence), even if the amplitude is not flattened.

Most amplifiers (and microphones and speakers!) do not treat all frequencies the same. For example, the amplifier may be able to amplify high frequencies better than low frequencies. Or it may not be able to react fast enough to amplify the high frequencies accurately. This is called frequency distortion.

We have already mentioned that microphones do not produce a current with the same phase of the original sound. Amplifiers also can have this problem depending on how they are constructed. If the phase of the output wave is not the same as the input source there is phase distortion in the output.

Sometimes electronics and software are used to intentionally modify a signal to make it sound different, as mentioned in Chapter 16. One example is adding in reverberation to make the recording sound more natural, as if it were recorded in a concert hall instead of a studio. The following two videos explain in detail one way reverb can be added to a recorded signal to make it sound like it was recorded somewhere other than a studio: Altiverb web site and The 3-D Audio and Applied Acoustics (3D3A) Laboratory at Princeton University web site. Commercial software is also available, for example Room EQ Wizard. Similar techniques can be used to improve the sound of an auditorium if electronic amplification is being used; signals from the microphones can be delayed or modified to provide a better interaction with the room acoustics.

18d: Speakers

A loudspeaker takes an electronic signal and turns it back into sound. How does a speaker reproduce sound from an electrical signal? We know from the previous chapter that the current flow in a coil of wire will produce a magnetic field. This electromagnet will attract or repel other magnets as if it were an ordinary magnet. One difference, however, is that we can easily reverse the polarity of the electromagnet by changing the direction of current flow. An oscillating current in the coil will result in an oscillating force if the coil is near a permanent magnet. This is the basis of a dynamic speaker. A coil surrounded by a permanent magnet is attached to a cone made of cardboard, plastic or other flexible material. When an oscillating electrical signal flows through the coil there is an oscillating force on the coil and cone. This makes the cone vibrate back and forth, producing sound waves in the air next to the cone.

Dynamic speakers have two basic designs depending on the range of sound frequencies being reproduced. Bass speakers or woofers have large, flat cones attached to the coil and are designed to produce low frequencies. A sketch and cutaway picture are shown below. The voice coil is attached to the cone or diaphragm. Electrical signals enter from the leads and go through thin wires which are glued to the spider, a lightweight flexible support system for the coil. Oscillating current in the voice coil causes an alternating magnetic force between the coil and the permanent magnet. This alternating force on the coil is transmitted to the cone which causes air to vibrate, creating sound.

Tweeters are designed similarly to bass speakers but have a small (2 cm to 5 cm), dome shaped vibrating part in place of the cone. Because they are smaller and lighter they are better able to produce higher frequencies. In both types of speakers the permanent magnet does not move. This is because magnets are heavy; if the permanent magnet was attached to the cone instead of the coil, the extra inertia would keep the cone from responding to fast variations in the signal.

It is also possible to make an electrostatic speaker that uses electrical forces, rather than magnetic forces. For this type of speaker, a thin sheet of flexible plastic (a diaphragm) with a metallic coating is suspended between two thin metal screens or grids. There is a small air gap between the grids and the plastic sheet. The sheet is charged by an external source and the oscillating signal is sent to the grids. The oscillating voltage between the grids causes the diaphragm to vibrate, producing sound. This is exactly the opposite process that occurs in an electrostatic microphone, described previously. An advantage of the electrostatic speaker is that it is very light and so responds very well to high frequencies. Another advantage is that, unlike a magnetic speaker where the sound comes from a small area, the area of the diaphragm can be quite large. The large area constitutes a less localized sound source making the sound seem more natural.

The idea of a speaker system is to try to trick the ear-brain system into perceiving the sound as if it were the original performance. Because we have an ear-brain system that incorporates sound from two ears, most sound recording and reproduction is in stereo which means two separate sound tracks are used. Sound is recorded from two or more microphones and mixed into two tracks which have slightly different sound. When the final recording is played back these tracks are fed to two separate speakers with the listener sitting somewhere between them. One potential problem with a two speaker system is phase. If the speakers are wired incorrectly, the left speaker can be out of phase with the right speaker causing destructive interference between the two sound sources. Some stereo systems have jacks for the speaker cables so that it isn't possible to connect them incorrectly. But if you are using free wires to connect your speakers you should connect them one way, listen to the sound, then reverse the leads to one of the speaker cabinets and listen again. The correctly wired case will sound louder, particularly for lower notes.

It is difficult to make a single speaker that can reproduce all frequencies equally well. To overcome this limitation bass and tweeters are often combined. The most common design is to have a pair of speaker boxes with one bass and one tweeter in each box. This requires a crossover circuit that separates the incoming signal into high frequencies (which go to the tweeter) and low frequencies (which go to the bass). Other designs have a third speaker to handle mid-range frequencies and a three-way crossover. Because low frequency sound has very large wavelengths it is difficult for the ear-brain system to accurately identify where the source is located. Modern speaker arrangements exploit this fact by having a single bass speaker (called a woofer or subwoofer) but a set of two mid-range tweeters to maintain the stereo effect. Modern speaker systems also often add two more speakers that are placed behind the listener to provide artificial reverberation. As we discussed in Chapter 17, our experience of sound direction depends to some degree on reverberation so that adding speakers behind the listener with a slight delay adds depth to the perception of sound from a stereo system.

Free-standing speakers do not sound very good, particularly for lower frequencies. When the speaker cone moves forward to produce a compression, the back side of the cone produces a rarefaction (a low pressure region). As the speaker vibrates compressions and rarefactions on the front side are exactly out of phase with the rarefactions and compressions coming from the back of the speaker. When sound from the back combines with sound from the front, the waves are out of phase and tend to cancel due to destructive interference as seen in the first figure on the left, below. This is very similar to the problem of the drum body that we saw in the previous chapter. The effect is more noticeable for lower frequencies which have longer wavelengths. This is especially a problem for the electrostatic speaker which typically does not have an enclosure and so does not produce low frequencies well.

There are several potential solutions to the problem of destructive interference between the back and front of the speaker. If the speaker is mounted in a wall or ceiling the sound from the back is trapped and cannot cancel sound from the front. This arrangement is called an infinite baffle and is shown in the second figure above. A second solution is to put the speaker in a box or speaker cabinet which has sound absorbing material inside so that the wave from the back is again trapped. This is shown in the third figure above. A third solution is to cause the sound from the back of the speaker to travel an extra half wavelength before it recombines with waves from the front. This is done by making a hole in the front of the speaker cabinet (sometimes called a bass reflex port or bass port or tuning port) and putting barriers inside the cabinet so that the sound has to travel an extra distance in order to exit as shown in the figure on the right, above. Obviously this extra distance can't be exactly half a wavelength for all the different wavelengths being produced but it can be arranged to emphasize a frequency range, typically lower notes where the destructive interference of a free standing speaker is more noticeable.

Another way of explaining how a bass port works is to think of the bass port as an opening to an enclosed volume of air. As we saw in Chapters 4 and 16, the opening will make a Helmholtz resonance frequency possible which depends on the size of the speaker cabinet. Choosing the right sized cabinet will reinforce certain low frequency notes in the music, giving a better bass response.

Video/audio examples:

Here is a simulation of a vibrating speaker from Wolfram (you may need to download their plug in to play with this demonstration).
A YouTube explanation of signal clipping (amplitude distortion) and its effect on a speaker.
Here is a YouTube video showing how a loudspeaker is made.
Here is a YouTube of how a electrostatic speaker is made.

18e: Transmission

Electronic signals may be transmitted as current flows in wires, pulses of light in fiber optic cables and by electromagnetic waves. There are three basic formats in which to send the information; amplitude modulation (AM), frequency modulation (FM), and phase modulation (digital).

As we saw earlier, a radio wave is emitted from an antenna when charge in the antenna is up and down as shown in the simulation of radio waves in Chapter 5. We can change the frequency of the emitted wave by changing the rate at which we move the charge in the antenna back and forth. The amplitude of the wave can be changed how far the charge moves up and down. Suppose you want to send a sine wave signal to the receiving antenna. The easiest way would be to simply move the charge in the antenna with the same frequency and amplitude as the sine wave you want to send. So far so good, the receiving antenna and amplification system can be tuned to that frequency. The problem comes when you want to send a different frequency. Then the receiving system has to tune to a new frequency. We know from Fourier analysis that sound (and therefor the electrical signal carrying it) can be thought of as a combination of many sine waves, each with a different amplitude and frequency. This causes a difficulty for the receiving antenna system because it can only be tuned to one frequency at a time.

In amplitude modulation (AM) a carrier wave with a constant frequency has its amplitude changed to encode the signal. The changing envelope of the carrier wave represents the signal being sent. The receiving antenna is tuned to the carrier frequency but the electronics on the receiving end decodes the amplitude as the signal and ignores the carrier frequency.

In frequency modulation (FM) the carrier's frequency is adjusted slightly up or down to indicate the signal being sent. The electronics on the receiving end interpret the slight variation in frequency as changes in the signal being transmitted. A simulation of both is shown below.

There are advantages and disadvantages to both AM and FM. The AM carrier signal uses longer wavelengths and these waves will reflect off a charged region in the upper atmosphere called the ionosphere. FM, which has shorter carrier wavelengths, does not. As a result, an FM station has to be in direct line of sight in order for the waves to be received. Cell phone and TV signals are also shorter wavelengths than AM and have the same problem; you have to be within sight of a cell tower or a TV tower to receive a signal. AM signals, on the other hand, because of their longer wavelengths (lower frequencies), will reflect off the ionosphere and can be received at long distances from their source, as seen in the diagram below. Shortwave radio and ham (amateur) radio use wavelengths only slightly shorter (wavelengths between AM and FM) than broadcast AM and can be transmitted around the world. Because the ionosphere is higher at night due to temperature changes and the effect of the sun on the layer, the range of AM, ham and shortwave reception improves at night.

An advantage of FM over AM is that FM can transmit a higher quality signal. If a signal varies too rapidly the signal amplitude might vary faster than the carrier frequency for AM. This does not happen with FM because the carrier wave has a higher frequency. The fact that the amplitude remains constant for FM also means the strength of the signal does not vary whereas a weak AM source might be lost at points where the signal amplitude is low.

A final difference in the quality of AM versus FM signals has to do with the effect of static from other sources such as lightning, car spark plugs and other random noise. Random electromagnetic noise will change the amplitude of both AM and FM carrier signals. But because the information resides in changes to the frequency of the carrier for FM, the quality of the signal is not as affected by changes in amplitude due to static noise.

Digital signals such as WiFi and Bluetooth involve sending a signal where the phase of the carrier wave is shifted relative to a reference wave. A code or key is set up in advance so that a particular shift in phase indicates a predetermined binary number. The phase shift is measured using a device called a lock-in amplifier that compares the arriving signal to a local reference frequency. Some digital signals involve sending several phase shifted frequencies at the same time at different carrier frequencies and there are several different ways to set up the key that matches the phase to a binary number. Digital signals typically use carrier waves of much higher frequencies than FM or AM so that information can be transmitted at a higher rate. As a result of the higher frequencies, however they suffer some of the same limitations of FM; the antennas must be in direct line of sight in order to communicate. Digital WiFi signals are also sent at much lower power than radio transmission and so are of short range, typically 30 m indoors and up to 100 m outdoors.

Summary

Recording generally starts with sound waves that are analog in nature. A microphone converts the vibrations in the air into an analog electrical signal; the amplitude and frequency of the electrical signal matches the sound amplitude and frequency. Vinyl and tape are analog recordings of the sound; the amplitude and frequency of the groove vibrations or the amplitude and frequency of the magnetic fields in the tape vary the same way as those of the sound source. For digital recordings the analog signal from the microphone is converted to a binary digital signal which is recorded as ones and zeros on a CD, DVD or disk drive. Electronic instruments create digital signals directly (MIDI) which can be recorded or manipulated with a computer. Digital signals are converted into analog signals, amplified and then sent to a speaker to convert them from electrical analog signals to sound vibrations. Here is a schematic of electronic recording and transmission.

Exercises: Electronics.