As Voyager 1 and 2 proceed further away do the radio waves red shift (change frequency)?
If so, then don't we have to compensate for that red shift by modulating the frequency so that it arrives at the expected frequency at the destination?
Theoretical Example: if the spacecraft is expecting 5.0 GHz then doesn't Earth have to transmit at 5.2 GHz to allow for the red shift?
Or am I confusing issues?
No, at the distances we have sent any spacecraft or probe to, there is no need to compensate for redshift (the Doppler effect) because a spacecraft is far away. Doppler shift is an effect of relative velocity, not distance.
The Doppler effect is defined such that the frequency $f$ as observed by a receiver moving at velocity $v_r$ relative to a source moving at velocity $v_s$ and where the source is transmitting at frequency $f_0$ is $$ f = \left( \frac{c + v_r}{c + v_s} \right) f_0 $$
In the case of radio transmissions, $c$ is the speed of light. $v_r$ and $v_s$ are measured in some inertial (that's basically a fancy word for "non-moving") reference frame.
For a stationary sender or receiver, simply set $v_s = 0$ or $v_r = 0$ respectively. From this it is obvious how, when both sender and receiver are stationary (in an inertial reference frame), the transmitted frequency equals the received frequency.
As you can see, for a given type of transmission (such as a radio transmission), only the relative velocities of the sender and receiver and the transmission frequency affect the received frequency.
This effect is caused by the fact that when the sender is moving toward the receiver, each wave front is closer to its neighboring wave fronts than merely its frequency would warrant. Likewise, when the two are moving away from each other, each wave front is farther away from its neighbors. Colloquially, the transmission is being "pushed together" or "dragged apart" by the relative movement of the sender and receiver. This is observed as a change in frequency at the receiver.
The distance between the two do not play a role in this effect, and thus we do not need to compensate for Doppler shift merely because an object is far away. We do however have to compensate for Doppler shift because the object is moving relative to us. Of course, because spacecraft generally move at relatively high speeds relative to an Earth ground station, in spacecraft communications we often do need to pay attention to Doppler shift, regardless of whether they are close to or far from Earth.
For example, if the spacecraft is moving away from the Sun at 15 km/s (not unreasonable at all for interplanetary missions) and Earth happens to be moving in the opposite direction at 30 km/s (which it does once a year), and the spacecraft is transmitting on 5 GHz, the frequency as received on Earth will be $$ f = \left( \frac{300~000~000 - 15~000}{300~000~000 + 30~000} \right) \times 5~000~000~000 \approx 4~999~250~075 $$ or approximately 4999.25 MHz instead of 5000.00 MHz. Conversely, if we want the spacecraft to receive our transmission on 5000.00 MHz, then we need to transmit at approximately 5000.75 MHz. If we didn't compensate for Doppler shift, we would need a receiver bandpass filter bandwidth of nearly a megahertz; enough to cram in two or three broadcast FM stations.
It's also worth keeping in mind that this is an issue not just for deep space missions. The math is a bit more involved because of the trigonometry to calculate the absolute value of the velocity and if you want an absolute value also compensating for the planet's rotation, but the exact same principles apply when a low orbit spacecraft is communicating with a ground station or for that matter with a spacecraft in a different orbit.
If we were to send spacecraft to other galaxies or even far-away stars, then Doppler shift due to the expansion of the universe might start to actually matter. However, for as long as it can be argued whether we have even exited our own solar system, the relative velocities caused by expansion of the universe are of magnitudes that are completely irrelevant for practical radio communications. The expansion of the universe is given as Hubble's constant $H_0$, and the most recent estimate for its value is $67~800 \pm 770$ m/s per megaparsec. The Voyagers are about 134 and 110 AU away, respectively, which works out to $6.497 \times 10^{-10}$ and $5.333 \times 10^{-10}$ megaparsec. If my math is right, taking Voyager 1 because it is farther away, this means an observed expansion rate of about 0.00004405 m/s (44 µm/s) corresponding to a received frequency of $$ \left( \frac{300~000~000}{300~000~000 + 0.00004405} \right) \times 5~000~000~000 = 4~999~999~999.999265833 $$ or a Doppler shift of about 0.001 Hz when the transmitted frequency is exactly 5 GHz. In other words, valid in theory but completely negligible in practice.
Contrary to the other answers, distance from the earth does does cause/influence red-shift (albeit indirectly). The universe is expanding away from us, and the further away a point in space is, the faster the expansion is at that point. The expansion rate is rather regular and predictable at macroscopic scales, so scientists actually use red-shifts of hydrogen emission spectra for distant stars to gauge how far stars and galaxies are from us.
If you had a spacecraft very, very far away, the universe's relative expansion to us would cause signals between us and the craft to be redshifted.
The expansion rate of our universe is usually given as Hubble's constant -- $H_0 = 67.15 (km/s)/Mpc$. We can calculate the velocity of the universe's expansion at a given distance as $H_0$ * the distance away.
Plugging in a distance like the distance to the closest star in wolfram alpha, we get that between us and Alpha Centauri, the universe is expanding at a rate of 0.2 miles per hour, or 0.3 kilometers per hour.
This is probably much lower than the actual relative velocity between us and Alpha Centurai just due to the fact that we're moving in different directions! So redshift will not be a significant factor if we ever decide to communicate to Alpha Centauri -- our actual relative velocities due to our relative motion will be more significant.
At intergalactic differences things might start getting a bit more noticeable. Between us and andromeda, the universe is expanding at a rate of about 53 km/s, about 120 million miles per hour, or about one ten thousandths of the speed of light. This is still not really enough to be terribly significant, I believe, but it does give a good scale as to how distance necessarily affects relative velocity and, indirectly, redshift.
EDIT A comment was made that reminded me that while expansion is homogeneous at the macroscopic level, the metric expansion of space might behave as homogeneously at sub-lightyear levels. I'm not familiar enough with this topic to give a definitive answer as to what models could be useful here.
Let me add to @Michael's answer by saying that this is also very much a factor when communicating with earth-orbiting satellites. For instance, the ISS signal bounces off a geostationary communications satellite before it (the signal) gets to the ground. If I recall correctly, these two spacecraft can differ in velocity up to 7 km/s. Not only can this cause either red or blue shift, but the Doppler shift varies dynamically during a single communication event. So Doppler handling is an important feature in the modems used to process these communications.
Yes and no. You have to take into account the time dilation (as in GPS clocks). Maybe the comm equipment does allow for some minor frequency change and it just accepts it still working. However as the gravity does not change in linear fashion, I think the biggest changes will be in LEO/GO. You have to calculate the time speed difference between "there" and "here". For LEO or similar (GPS orbits) it's about ~38us per day. Diffrent time speed is visible in microwave radiation as redshift/blueshift. Not "speed" of the wave.
