Effect of time dilation on Earth/space communication?

[InquiringMind]

Let's say there is an audio oscillator on earth sending a 440 Hz audio tone over radio to a spacecraft. There is also an audio oscillator on the spacecraft sending a 440 Hz audio tone over radio to earth. Time is slower in the high gravity of earth than the weak gravity in space. Is the 440 Hz signal received by the spacecraft less than 440 Hz and the 440 Hz signal received on earth greater than 440 hz.

If there is a shift in audio frequency, I would think it would change the pitch of an astronaut's voice heard on earth (it would be higher pitched) and the voice of someone on earth would be heard at a lower pitch by an astronaut. Does this happen, or is the shift too small to be noticed?

 

[anuttarasammyak]

As you assumed, as for the Earth, red-shift for outgoing and blue-shift for incoming lights take place. The shifts are measurable and well conidered in GPS satellite design for an example. I am not a expert of human listening physiology enough to tell you whether ears can distinguish it or not.

 

[PeroK]

Let's say there is an audio oscillator on earth sending a 440 Hz audio tone over radio to a spacecraft. There is also an audio oscillator on the spacecraft sending a 440 Hz audio tone over radio to earth. Time is slower in the high gravity of earth than the weak gravity in space. Is the 440 Hz signal received by the spacecraft less than 440 Hz and the 440 Hz signal received on earth greater than 440 hz.

If there is a shift in audio frequency, I would think it would change the pitch of an astronaut's voice heard on earth (it would be higher pitched) and the voice of someone on earth would be heard at a lower pitch by an astronaut. Does this happen, or is the shift too small to be noticed?

It depends how the audio signal is encoded. The underlying radio signal would be blue/red shifted, but whether this results in the encoded voice message being changed depends on the technology.

The gravitational redshift of the radio signal between Earth and a spacecraft would be negligible.

If the spacecraft was moving at relativistic speed relative to Earth, then there might be a significant red/blue shift in the underlying radio signals. But, the technology could take that into account when decoding a voice message.

 

[Borek]

Shouldn't be difficult to calculate. I wonder if the Doppler effect won't be more prominent though.

 

[jbriggs444]

Shouldn't be difficult to calculate. I wonder if the Doppler effect won't be more prominent though.

For weak fields, we can factor the predicted effect into components from two primary sources: kinematic (relativistic Doppler) and general relativity (gravitational red/blue shift).

A full computation from General Relativity would combine the two effects in a non-linear way. But for the weak field of the Earth, we can compute the effects separately and simply add them together.

I would expect fore-and-aft relativistic Doppler to dominate for most listening angles. When the space craft is approaching, you get blue shift. When departing, you get red shift.

When the craft is directly overhead in low earth orbit then transverse relativistic doppler yields a red shift. For low earth orbit, this effect dominates over gravitational blue shift. For a sufficiently high orbit it is gravitational blue shift that wins instead.

I recall a fairly recent thread about the crossover altitude where the kinematic and gravitational effects cancel, but I no longer recall the title. For GPS satellites, the net red shift is about 7 microseconds per day. Which is utterly negligible for purposes of listening to a 440 Hz tuning fork.

 

[Klystron]

Digitally encoded transmitted messages, including human voice, should not be altered by the processes described in the original post.

Transmission Control Protocol -- Internet Protocol (TCP-IP) packets, for example, contain error detection that improve data integrity regardless of changing signal characteristics assuming reliable connection. The connectionless User Data Protocol (UDP) provides enhanced error detection including checksums suitable to carry Real-Time Transport Protocol (RTP) designed to carry information such as real-time voice/image streams.

Returning to the original 440hz signal deployed as carrier then modulating human voice on or within it, optimum methods suggest comparing amplitude with frequency modulation (AM / FM) techniques in the discussion. Radial relative motion toward and away from an emitter should affect AM receiver fidelity to a greater extent while frequency shifts as described in prior posts will require interesting error correction for FM receivers.

Terrestrial FM radio receivers certainly benefited from automatic frequency control (AFC) circuits that compensate for carrier frequency fade, waver, shifts and related interference. The interesting question of detecting corresponding changes in perceived pitch of a modulated analog voice might be subsumed in the loss of fidelity.

IOW Yes, I have heard changes in pitch of broadcast voice and music due to relative motion and during TX/RX glitches, but attendant loss of volume and static interference compared to perceived pitch renders the question somewhat academic, if not moot. Correcting the signal, including for relative motions of TX and RX, should preclude voice distortion, at least from regular motion.