I always pump my tyres up to the maximum (like 45 bar), for maximum fuel economy.
However, does this affect road noise?
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tl dr; More pressure = less noise.
Here is a pretty good write-up about the affects of tire noise. In the write-up it states the following:
Tires running higher inflation pressures generate lower noise levels compared to those with lower inflation levels.
This holds true to my line of thought because a flat tire (or very low tire) will make a lot more noise than a full tire will. According to the write-up, one of the reasons noise is created by tires is because air gets trapped within the tread pattern as the tire rolls onto the pavement and the car is pressing down upon the tire. As the tire rolls forward, the air is released and makes noise. This is reduced when the tire is fully inflated versus one which is low on air pressure.
There are many reasons for tire noise, but needless to say, tire pressure is one of the factors of road noise.
Tyres pumped up to 45 bar would probably explode... What car do you have, as even 45psi sounds high for a normal car?
You should always inflate your tyres to the manufacturer's recommended pressure. Over-inflating will lead to increased wear (so you'll have to replace them more quickly, negating any fuel saving!), and poorer grip and handling, leading to increased skid risk... Under-inflating has equally bad problems...
I've recently (in the last three months) started running my tyres at relatively high pressure on my daily driver as I'm a hypermiler and higher pressure does indeed decrease rolling resistance and improve in-gear coasting range. Obviously I never exceed the manufacturers stated maximum printed on the sidewall.
I have not noticed and appreciable difference in tyre noise at all so suspect that in most cases, higher pressure will not lead to any increase in cabin noise and if it does, the cause should definitely be investigated.
I have had many cars over the years and have found that tyre (rubber) quality can have a lot to do with noise as well. I bought my current vehicle about one year ago. It was less than one year old. It was used by the dealer manager. After a few months I started getting road noise from the tyres. Upon inspection I found that the tyres were over 5 years old and the rubber was loosing it's integrity. So it is not just a matter of tyre pressure. You need to check it all.