We had one of these. Our house was remodeled in 1963 and we got the Tappan dishwasher as well as the nifty Tappan electric rotisserie wall oven and Nutone fold-away range hood! I think they were all yellow.
There was a textured grayish panel where the controls were, and metal vent slots across the top. I guess the big drum was quiet. It had a rough surface so it actually did sling the water around a bit. The water level had to be just right. If it wasn't, the drum made a wave-like whooshing noise as it kicked up all the water, ran dry for a second, and then kicked it up again after enough water collected back in the tub.
That little box on the front of the rack in the picture was the powder detergent dispenser. It was split in the middle with metal screens on the bottom, and the drum spray would hit the bottom and dissolve the soap. Sometimes they didn't empty all the way. The drum was also spinning during the drying cycle, presumable blowing air around, and always sending a little vibration through the counter top.
There was something weird about how the door opened. The chrome trim around the control panel was also part of the latching mechanism and it all pulled outward with the handle. I might be wrong on that though. I recall my dad doing a number of repairs on the machine, and it was used into the 1970s when it finally rusted through.