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I fish with a radio playing 90% of the time while fishing and still catch. Heck, I have two wet sound 6.5" speakers mounted in my current boat with a amp powering them. What I do though while fishing is have the bass turned all the way down and only keep the volume on to where I can barely hear it. I do believe if you can feel the vibrations from your music/radio in the boat, the fish can sense it as well. Everyone has their own take on it.
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I too fish with a radio. Keep volume where only I can hear it. I do shut motor down at least 50 yds from where I plan to start and ease in. Had a boat this weekend pull up not 50 ft from me and shut down while I was anchored but I caught and they didn't. Mean looks didn't seem to bother them.
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I catch just a few fish with the radio on as I do with it off