Why did Sputnik-1 transmit on both 20 and 40 MHz?

Question

Wikipedia's Sputnik 1 and this answer to Why did Sputnik 1 have four antennas? say that Sputnik transmitted at both 20 and 40 MHz.

Why two different frequencies? Why so far apart?

It's worth noting that the ionosphere's transparency is sometimes very low at 20 MHz; the 10 meter or 30 MHz band of amateur radio relies on ionospheric reflection for long distance communications, so sometimes 20 MHz wouldn't even be useful for orbit-to-ground communications, and 40 MHz is not likely to have been available on most home short wave radios (for the same reasons).

Answer 1

Russian version of Sputnik-1 Wikipedia article has the section labeled "Sounds of Sputnik" and cites the respective technical report regarding development of the Sputnik's "radio device" D-200 (in Russian).

According to the report, primary reason for transmitting on two frequencies was redundancy. The transmission frequency had to be higher than that of the highest critical frequency of ionosphere's F-layer, which was estimated as 15MHz, but transmission frequency was chosen at 20.005MHz due to the limit of Soviet direction finder "Krug". The second frequency was just arbitrarily chosen to be 2 to 3 times higher because it would allow for longer receival duration compared to the first frequency.

Wikipedia article gives the brief summary of the basis of frequencies choice (translated from Russian):

Parameters of the [signal] transmission (power and frequencies) were selected based on the [respective parameters of available] widespread receivers of Soviet and foreign amateur radio enthusiasts, in order to obtain new information about the ionosphere structure from mass amateur observations ([such as] difference in the times of appearance and disappearance of signals at two frequencies, relative level of the signal, Doppler shift).

• The frequency of the VHF (ultra-short wave) signal (40.002 MHz) is on the edge [i.e. limit, borderline] of the amateur seven-meter range and does not get reflected from the ionosphere in a wide cone;

• the frequency of the HF (short wave) signal (20.005 MHz), although being higher than the predicted critical frequency of the ionosphere F layer at winter noon of 1957-1958 (up to 15 MHz), is still close enough for the signal to undergo significant attenuation [or damping] in the F layer (about 10 dB ), and in the case of an oblique incidence [of the signal] to be reflected.

Therefore, conditions for propagation of Sputnik's radio signals in ionosphere at the selected two frequencies were significantly different, hence allowed the use of ground-based observations (including mass amateur radio observations) to probe through the ionosphere, which was impossible before the launch of the Sputnik.

The source also describes distances at which the signal was recieved:

Satellite signals were firmly received using conventional amateur radio equipment at a distance of up to 2-3 thousand kilometers; [some] cases of extra long [-range] reception at distances up to 10 thousand km were recorded.

P.S. As I'm not an expert in radioelectronics, some technical terms might be not 100% correctly translated.

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Below is original text in Russian:

Параметры излучения (мощность, частоты) были выбраны из расчёта на широко распространённые приёмники советских и зарубежных радиолюбителей, чтобы из массовых любительских наблюдений (разница времени появления и исчезновения сигналов на двух частотах, относительный уровень сигналов, доплеровский сдвиг) получить новые сведения о структуре ионосферы.

• Частота УКВ сигнала (40,002 МГц) находится на границе любительского семиметрового диапазона и не отражается от ионосферы в широком конусе;

• частота КВ сигнала (20,005 МГц), хотя и выше прогнозировавшейся критической частоты слоя F ионосферы в зимний полдень 1957—1958 года (до 15 МГц), всё же достаточно близка к ней, чтобы сигнал претерпевал значительное затухание в слое F (около 10 дБ), а при косом падении отражался.

Таким образом, условия распространения радиосигналов спутника в ионосфере на двух использовавшихся частотах были существенно различны и позволяли использовать наземные наблюдения (включая массовые наблюдения радиолюбителей) для зондирования ионосферы «насквозь», что было невозможно до запуска спутника.

Приём сигналов спутника уверенно осуществлялся с помощью обычной радиолюбительской аппаратуры на расстоянии до 2—3 тысяч километров; были зафиксированы случаи сверхдальнего приёма на расстояниях до 10 тысяч км

Answer 2

The following is (now apparently disproven) speculation based on some very basic radio theory rather than any particular knowledge of Sputnik 1. It should be disregarded if someone with knowledge of the actual circuits in use has better information. I did some web searching but did not find any descriptions of Sputnik 1 that provided good evidence for or against the below theory about its construction.

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If we suppose that 40 MHz is not chosen for reception reasons, then the obvious reason to choose 40 MHz is that it is the second harmonic of 20 MHz. An oscillator generally produces some amount of signal at harmonics of the original frequency (small or large depending on its design), and certain RF circuit elements such as stubs (and, with some complications, antennas) also work with harmonics as with the fundamental. Therefore, components could be shared between the 40 MHz and 20 MHz systems, thus saving weight and complexity.

[Further information indicates that this was not the case — the 20 and 40 Mhz transmitters were separate, and considered redundant systems to each other. There still might have been some design reason to use an approximate multiple, but I can't say what exactly they might be.]

Furthermore,

Signals on the first frequency were transmitted in 0.3 s pulses … with pauses of the same duration filled by pulses on the second frequency. [Wikipedia]

While this alternation could be purely to even out the power draw, it also suggests that there might not be two independent transmitters, but one transmitter which either produced both signals at once in the oscillator, followed by a switchable filter to select one of them to send to the power amplifier or antennas, or the oscillator itself could be modulated to switch between those frequencies.

Sputnik is said in Wikipedia and a citation behind paywall to have transmitted on "20.005 and 40.002 MHz". Of course, 20.005 × 2 = 40.010, not 40.002. But this does not mean harmonics are not applicable; under the theory that the second harmonic was being used to generate the 40 MHz signal, it is reasonably plausible that when the transmitter switched between the 20 MHz and 40 MHz conditions, secondary effects (changes in loading of circuits, etc) caused a slight frequency shift; or, if the oscillator is modulated, it's merely error or a free choice in the designed tuning, and the requirement is only that the second frequency be approximately a multiple of the first.

I don't know what the actual components of a one-watt tube-based transmitter of the time would be, so I don't know how plausible either of these hypotheses is. [Plausible, perhaps, but apparently false.]