First time I heard that a five-watt CW (Continuous Wave, or "Morse Code") radio could reach any part of the world, I thought it was just ramblings of an aging ham radio operator.
But it is actually very easy to prove that it is possible, and long distances may be achieved even with 2W or 1W. The secret is the narrow bandwidth. AM broadcast radio needs 20KHz per station. SSB radio needs 5KHz. CW needs zero, in principle. A CW transmission is like a laser: all the power is concentrated on a single color hue, while SSB is a white light that spreads energy thin on all possible colors.
In practice the band is (at most) 100Hz for Morse code, because CW is not really CW, it is keyed on and off. It is equivalent to the AM-SC modulation of a very low frequency signal.
Doing some math, we find that, given the same transmission power, CW has a gain of at least 20 times over SSB (5000 ÷ 100). Colloquially, people say that 5W CW is equivalent to 100W SSB. But Morse can pass through bandwidths narrower than 100Hz, in particular when operators use "slow code"; so the CW gain is generally well above 20.
Digital modes are very economical on bandwidth as well, with PSK31 using just 31Hz! Other modes need more bandwidth (in exchange for faster data rates). The narrow bandwidth and automated reception (no need for a human trained in Morse at RX) create even more opportunities for QRP (low-power transmission). QRP also means cheaper transmitters, batteries, solar power, etc.
In a Zen koan (roughly analog to Christian parable), the master asks the apprentice what is the sound of one hand clapping. Likewise, the CW signal seems to have no sound, because it is a pure carrier, it has no defined pitch.
In order to hear Morse code, the receiver must be slightly off-tune. For example, if the transmission is made at 9998.0KHz, the receiver could be e.g. at 9998.8Khz. The product of the local carrier (known as BFO) and the remote signal generates 800Hz tones (9998800 minus 9998000). Receiving at 9997.2KHz would work as well.
The math is exactly the same as if the radio was receiving a pure 800Hz tone over SSB. In CW, the standard is to take the incoming signal as if it were upper sideband (USB). The CW signal comes in 9998.0Khz, so the hypothetical carrier, that we should set our BFO onto, is 9997.2KHz. The CW etiquette also specifies the first transmitter (the guy that calls "CQ CQ CQ...") owns the frequency. Whoever answers to the CQ is in charge of tuning his BFO.
The CQ guy is transmitting at 9998.0Khz, but he must also receive in an offset frequency in order to hear audio. Let's say he prefers 1000Hz tones, so he tunes his radio to 9997KHz. But he will only hear 1000Hz tones if the responder transmits on 9998.0KHz as well. If the responder does the math wrong and transmits in 9998.8KHz, the CQ guy will hear unpleasant 1800Hz beeps.
Modern CW radios can be configured a "spot tone", meaning the desired beep pitch. The display shows the center CW frequency, and the receiver offset is automatically set. The only thing the operator must do is to fine-tune the frequency while pressing the SPOT button until the button beep has the same pitch as the received Morse beeps.
The operator must also be sure that pitch *decreases* when frequency is slightly increased — meaning that USB convention is being followed and BFO frequency is below CW frequency.
This means that you are "zero beat" with transmitter, that is, your transmitting frequency is exactly the same as the other side — as we said, it is good because it allows the remote operator to hear Morse in his own favorite pitch.
And yes, you may hear many other Morse conversations with different pitches while you do your own conversation, in particular when your radio does not have a sharp filter around the BFO frequency (case of simple kit radios). But the unfiltered audio is useful while looking for counterparties, so the filter should be togglable/configurable.
The applet below generates a beep-beep CW with random frequency around 10KHz. The spot tone is fixed at 800Hz. The slider allows you to set your transmission frequency, and Spot Tone button plays (unsurprisingly) the spot tone. Play with them until received pitch equals the spot tone, and your transmission frequency is near or at the received frequency.