A. Let me begin by applauding your flight instructor's efforts to keep noise to a minimum. Many instructors fail to teach their students about the importance of noise abatement, making airports bad neighbors in the eyes of those who live or work nearby.
Reducing propeller rpm does reduce both horsepower and climb performance. It is preferable to climb using a higher rpm while keeping in mind the effect it is having on the neighbors.
If the redline on your Cherokee 235 is 2,700 rpm, I wouldn't pull the propeller back below 2,500 rpm after takeoff. If the redline is 2,575, I'd pull back to 2,400 rpm. If you need more power to outclimb an obstacle, by all means use everything you've got. For climbing to a different altitude when the climb rate is not especially critical, you could increase the power by 100 rpm or so. Don't be surprised if you need to use full power to climb at high density altitudes as your Cherokee 235 may have trouble climbing much above 10,000 feet.
Although it is important to keep noise issues in mind any time you are flying in a populated area-especially at low altitudes and high power settings such as during takeoff and climbout-you are by no means the noisiest airplane in the pattern. Your Cherokee 235 does not make as much noise as other popular airplanes such as a Cessna 206, Cessna 210, or Beech Bonanza. Your airplane also climbs very well, making it higher than many other airplanes by the time it passes over noise-sensitive areas. Simply using the best climb angle and power setting to gain altitude quickly when you are approaching noise sensitive areas may help reduce noise levels for the neighbors