Every sound after takeoff, and why it is normal

The first few minutes after takeoff are full of new noises. Each one has a simple, routine reason, and they happen on almost every flight.

During the takeoff run

A deep roar and being pressed into your seat: Takeoff power. The push you feel is the plane accelerating, much like a fast car, though gentler.
The rumbling suddenly stops: The wheels have left the runway. That smoothness is the moment you are flying.

A clunk or thump a few seconds later: The landing gear folding up into the plane, then its doors closing. It can be surprisingly loud, and it happens on every flight.
The engines get quieter, and you feel a slight sinking: Shortly after takeoff the pilots reduce from takeoff power to climb power. The plane is still climbing. Many people feel this as slowing down, and it is completely routine.
Whirring again, then a gentle settle: The flaps on the back of the wings retracting in stages as the plane speeds up. Each stage can feel like a tiny dip.

The plane banks into a turn: Following the departure route. Turns in passenger jets are gentle, usually well under a 30° tilt, though looking out of the window makes them seem steeper.
A chime: Chimes are signals between the pilots and the crew, or for the seatbelt sign. They are routine messages, not alarms.
Ears feeling full: The cabin pressure changing gradually as you climb. Swallowing or yawning helps.

If a sound surprises you, notice that the crew carry on as normal. They hear the same sounds on every flight, several times a day.