on is not one of how far apart two signals are in
number of cycles per second. The question always is: How large in
percent is the difference between the two frequencies? The matter of
separating two effects of different frequencies is a question of the
"interval" between the frequencies. To find the interval between two
frequencies we divide one by the other. You can see that if the quotient
is larger than 1.1 or smaller than 0.9 the frequencies differ by ten
percent or more. The higher the frequency the larger the number of
cycles which is represented by a given size of interval.

While I am writing of frequency intervals I want to tell you one thing
more of importance. You remember that in human speech there may enter,
and be necessary, any frequency between about 200 and 2000 cycles a
second. That we might call the range of the necessary notes in the
voice. Whenever we want a good reproduction of the voice we must
reproduce all the frequencies in this range.

Suppose we have a radio-current of 100,000 cycles modulated by the
frequencies in the voice range. We find in the output of our
transmitting set not only a current of 100,000 cycles but currents in
two other ranges of frequencies. One of these is above the signal
frequency and extends from 100,200 to 102,000 cycles. The other is the
same amount below and extends from 98,000 to 99,800 cycles. We say there
is an upper and a lower "band of frequencies."

All these currents are in the complex wave which comes from the
radio-transmitter. For this statement you will have to take my word
until you can handle the form of mathematics known as "trigonometry."
When we receive at the distant station we receive not only currents of
the signal frequency but also currents whose frequencies lie in these
"side-bands."

No matter what radio-frequency we may use we must transmit and receive
side-bands of this range if we use the apparatus I have described in
the past letters. You can see what that means. Suppose we transmit at a
radio-frequency of 50,000 cycles and modulate that with speech. We
shall really need all the range from 48,000 cycles to 52,000 cycles for
one telephone message. On the other hand if we modulated a 500,000
cycle wave by speech the side-bands are from 498,000 to 499,800 and
500,200 to 502,000 cycles. If we transmit at 50,000 cycles, that is, at
6000 meters, we really need all the range between 5770 meters and 6250
meters, as you can see by the frequenc