Have a 2013 Honda Fit (base model) with 125k miles. There is a strange sound that the car makes as it accelerates and it gets loud inside the cabin that is deafening. is NOT high pitch sound or ticking or grinding sound. More like " aahh" up and down sound, then aaahhh, then aaah louder and louder. Also notice the sound gets louder as the car turns a bend and moving. It like echo’s the sound even louder. I have not taken it to the mechanic but looking for advice here as to what it might be and the cost if it is that.
Again is the sound is NOT , a creaking, clunking, or popping sound or whining sound , or a crunching noise, or a screeching sound.
Diagnosing a car based on a written sound description over the internet is a wild-donkey guess at the very best. Guessing the repair cost is an even wilder guess considering the cost of repairs varies greatly based on where you live. Repair costs in New York City are not the same as Mexico City.
Sorry can’t be of more help. Having a professional actually hear the car is your best bet. You can always say “No thanks” and take it elsewhere for another estimate.
My daughter has constant wheel bearing failure with her Fit. Maybe you should take a trip to the auto mechanic for diagnostic. Hers happened at 65k and again at 125k.