Whirring sound

I have a 2006 honda accord with about 65k miles on it. Off late, i have been hearing a distinct whirring sound when i turn the key on. this sound gets louder as and when i accelerate and fades out. please help me identify the problem. Many thanks.

Just when you turn the key on? not accessory position, but the on with the dashboard lit up? The fuel pump should be the only whirring you hear. If it’s getting louder and louder, it could be failing.

We really need the OP to clarify when this noise is heard, as well as where it seems to be emanating from.

Is it just when turning the ignition key?
Does it also take place as you accelerate, as you seem to imply?
Is the noise heard continually from the time that you turn the ignition key to when you drive, or is it intermittent?
Does the ambient temperature seem to have any impact on the noise?
When does it fade out? At what speed, and under what conditions?
Does the noise return when you slow down? At what speed, and under what conditions?