Why does my car make noise in reverse?
I presume from your question, "Why does my car make noise in reverse?", you are not referring to a noise that the transmission has suddenly begun to make, but rather why does the car make noise in reverse gear and not the forward gears.
The name of the noise you hear is called "gear whine", and it is a common property of ordinary straight cut spur gears. This used to be very common on cars with manual transmissions, as all of the lower reduction gears were spur gears. In American cars, which had three-speed transmissions, you would hear a whine in first and second gear. Third gear was silent as in this gearshift position you were in direct drive and a gear reduction (other than that in the differential) was not involved. If you do not remember what cars of the 1940's and 1950's sounded like, you can experience if by watching street scenes from classic movies. Every time a car pulls away from the curb you will hear a distinctive lower gear whine.
The gear whine could be reduced or eliminated by employing helically cut rather than straight cut spur gears. The reason helical gears run silently is because the engagement of each of the gear teeth is gradual. These helical "silent gears" came to be adopted for second gear in the three-speed transmissions of better cars.
The problem was that helical gears are both more expensive to machine and generally take up more space in a transmission case. Therefore, as a reasonable cost saving measure, many car builders chose to use the more expensive helical gears only for those gears in which it was presumed that the driver would commonly use for motoring, i.e., second gear in the American three-speed transmission and second and third gear in the European four-speed transmission.
To operate a car in reverse an additional gear has to be inserted into the car's gear train. This gear took up extra room on the gear case, and it would be seldom used. There was, thus, a reason to avoid, and no need to use, a helical gear set for reverse. The driver would not spend a great deal of time motoring about while looking backward. So the whine of a spur gear would not be objectionable.
I recently had the opportunity to drive a classic Citroen 2CV at an event sponsored but the Lane Motor Museum in Nashville. (Note: The Lane Motor Museum is one of most enjoyable and interesting automobile museums on the planet. Go there.) I was delighted to experience the loud and distinctive gear whine of the transmission's straight cut spur gears in first and second gears of the four-speed gearbox. To gear heads, that might be amusing. For it was Citroen that pioneered the production machining of helical gears. In fact the multi-chevron Citroen logo depicts the tooth pattern of a helically cut gear.
The forward gears use helical-cut teeth which mesh more quietly and wear more slowly than straight-cut teeth. Reverse, being used a much smaller portion of the time, uses straight-cut teeth to save a few cents of manufacturing cost.
I assume you have a manual transmission or a Honda (Honda automatics are built much like manual transmissions).
The answer is because reverse gears are dog cut gears. This means that the teeth are flat and contact another flat gear. This makes them very strong, but also makes them noisy. So, you have noise in reverse.
Most probably it is that your car does not go in reverse very much of the time so the gears don't get to know one another very well. The forward gears wear to a perfect fit and will run quieter. Just like a tractor that never uses certain gears which will be noisy until they get used a lot. Forward and reverse have nothing to do with it.
The chances are that it has straight cut reverse gears. While the forward gears engage via synchromesh clutches, reverse actually needs an idler to be shifted into place. Helical gears will produce enough axial thrust to push themsrlves out of engagement, so straight cut gears are used. The downside is that they whine a bit.