In the previous section we introduced a very specific example of feedback in an acoustic cavity. Actually, there are many examples of feedback and they fall into two categories: positive and negative feedback. In any feedback loop, the output of the loop goes around to modify the input to the loop. Of course, since it is a loop, there really is no separate input or output. When the loop modifies the signal, it can either exaggerate the signal or minimize the signal. The first case is positive feedback and the second case is negative.

The acoustic cavities discussed in the last section are a perfect example of positive feedback. Above, we stated that positive feedback exaggerates the signal. Let’s consider the case of acoustic feedback where the overall gain is say 1.5, and we start with a signal of 0.1 V. After one loop, the signal will be 0.15 V, and in the next loop, the signal is 0.225 V. Thus, if the signal is getting bigger, it continues to get bigger. In other words, it exaggerates the signal. Now, if the gain is 0.5, after one loop, the signal will be 0.05 V after one loop, and 0.025 V after the next loop. Here if the signal is getting smaller, it continues to get smaller – again, the loop exaggerates the effect.

One other example of positive feedback is explosions – either chemical or nuclear. In any explosion, energy stored in a molecule or a nucleus is released. However, the energy stored in any signal molecule or nucleus is very small. What is needed for an explosion is for all the particles to release their energy at the same time. This is done through feedback. The idea is that if one particle releases its energy, it makes it more likely that other particles will release their energy, as well. In a chemical reaction, this occurs because the temperature starts to increase and the increasing energy makes it more likely that other molecules will release their energy. Of course, this further increases the temperature, making it even more likely that other molecules will give up their energy, etc. When a nucleus releases energy it gives off neutrons. However, a neutron can encourage another nucleus to release energy and more neutrons. Thus, the number of neutrons starts to increase, making more likely that more nuclei will give up more neutrons, etc. This feedback can occur very quickly, leading to an explosion.

While a system with positive feedback can change very quickly (i.e. the amount of sound in the cavity, the temperature of a sample, or the number of neutron) a system with negative feedback does not like to change, and this is a very important property. For example, one wants to keep the temperature of their house constant. This is done through negative feedback. The loop consists of the following elements:

A thermometer – to measure the house temperature
A thermostat – to control the furnace based on the thermometer
A furnace and air conditioner – to heat and cool air for the house
The air in the house, which affects your temperature.

What happens if the temperature of the air starts to fall? The thermometer will measure this and tell the thermostat to switch on the furnace. The furnace will then heat the air and reverse the fall in the temperature. If the temperature rises above a certain level, this affects the thermometer, which will trigger the thermostat which will tell the air conditioner to turn on, which will reduce the temperature. In all cases, the response of the feedback loop is opposite to the change: if the temperature rises, the system responds by reducing the temperature. If the temperature falls, the system responds by increasing the temperature. Thus, negative feedback loops are a way of maintaining a system in a constant states.

What would happen if the heating system in your house had positive feedback? If the temperature started to rise, the furnace would turn on, further increasing the temperature. If the temperature fell, the air conditioner would come further decreasing the temperature. Thus, positive feedback creates very unstable conditions, while negative feedback creates stable conditions.

Another amazing example of feedback is the temperature of the human body. We expose our body to very hot weather (over 100° F) to very cold temperatures (under 0° F) but our internal temperature is maintained at 98.6° F within a few tenths of a degree. Of course, under extreme conditions, the body cannot maintain this indefinitely, but it generally controls this temperature very precisely. This can only be done through feedback.

Perhaps the most significant lesson from feedback is that it shows the importance of spectroscopy and a way of producing a frequency source.

Until the lab on feedback, we often talked about frequencies, and used the frequency generator in the computer, but we had no understanding of how frequencies are generated in the first place.

We found that putting the acoustic cavity into feedback produced a sound at a definite frequency, but we did not know which frequency it would produce. However, since we know how to calculate the overtones of an acoustic cavity, we could show that feedback always occurs on a cavity mode. With this observation, we now have a method for producing a particular frequency. First, you design a cavity where the desired frequency is the fundamental or overtone of the cavity. Then, you put the cavity into a feedback loop with sufficiently high gain. Finally, you need to make sure that the feedback picks the mode that you want. This is the hardest part, as it is hard to predict which mode will go into feedback. However, by analyzing the nodal lines of each mode, you can probably pick a spot where the desired mode is preferred.

This is exactly how a quartz crystal watch works – although here, the cavity is the quartz crystal and the sound waves are in the crystal.

This is also how instruments work. Essentially, an instrument faces the same problem as a clock. On an instrument, you want to play a note of a certain pitch. That pitch corresponds to a frequency – but how do you get the particular frequency that you want? You must build a structure (the instrument) that has cavity modes that correspond to the frequency that you want. This can be done with the modes of a vibrating string or an air column. Then, there must be some feedback loop to set that particular mode vibrating. The contact point between the bow and the string in a violin provides that feedback, while the reeds in an oboe or clarinet, or your lips of a flute or brass instrument provide the feedback.

One problem common to all frequency sources is that they can be affected by external conditions, such as temperature. In an acoustic cavity, the speed of sound depends on temperature that can affect the frequency of the cavity modes. Of course, feedback can also solve this problem – with negative feedback and a heater, the cavity can be maintained at a constant temperature.

Also, the composition of the air in the cavity can affect the frequency. This is easily solved by filling the cavity with a know gas and sealing it up. On the other hand, it provides a way of detecting changes in the air composition. If you add some helium to the cavity, the speed of wound will increase and the pitch will go up.