Consider a bell and a microphone separated by 4.2 sound-years in a universe filled with air. In said universe one sound-year = 343 m/s x 3600 sec/hr x 24 hr/day x 365.25 days/year = 1.08 x 10^10 meters. The bell and the speaker always remain at rest wrt their own co-moving coordinate system. The bell is located at the origin and the microphone is located 4.2 sound-years in the positive-x direction. If the bell begins to ring, the first clang of the bell will not be picked up by the microphone until 4.2 years have passed.

Now consider a distant observer located on the x-axis several more sound-years beyond the microphone in the positive-x direction. We now accelerate the bell and microphone until they are traveling at 0.867 times the speed of sound towards the distant observer who is at rest with respect to the bell and microphone. How far will the bell have had to have been from the distant observer when its first clang sounded in order for the first clang and the distant observer to arrive at the microphone simultaneously?

Silvia provides an answer [ with Dolan's re-works in brackets ] :

If we let the distance away that [ the bell ] was when the [ first clang ] departed be d, we can see that the time that [ the bell ] took to get from distance d to its present position of [ 4.2 sound-years from the observer ] must equal the time it took for the [ sound of the first clang ] to get from distance d to the observer. That is:

(d - 4.2) / v = d / s

s is the speed of sound, v = is 0.867s, and s = 1.

(d - 4.2) / 0.867 = d / 1

d - 4.2 = 0.867 * d

d * (1 - 0.867) = 4.2

d = 4.2 / ( 1 - 0.867)

d = 31.6 sound-years

So in the observer's frame the [ first clang ] has taken 31.6 years to arrive,
and there are many more than 4.2 years worth of clangs between [ the bell ] and the observer.

We now repeat the experiment. But this time we accelerate the observer until he is traveling at 0.867 times the speed of sound towards the bell and microphone, which are at rest. This time the observer only needs to be 4.2/0.867 = 4.84 sound-years away from the microphone when the first clang sounds in order to arrive at the microphone simultaneously with the first clang. And when he does arrive there will be exactly 4.2 years worth of clangs between the bell and the microphone/observer.

The two cases lack symmetry. The same lack of symmetry pertains in the Helical Path Paradox when Big Ben (the earth) and Proxima Centauri are accelerated versus the observer being accelerated instead.