Why does sound bounce off the open end of a tube ?

Blow up a balloon.
Prick the balloon with a pin.
BANG!

The air inside the balloon is compressed to a pressure above atmospheric pressure by the stretched rubber of the balloon. (photo of partly broken balloon)

When the rubber wall of the balloon breaks, the compressed air expands.
As long as the pressure of the air inside the balloon (or more accurately where the balloon was) is above atmospheric pressure, the air accelerates outward.
The air rushing outward reaches maximum speed just as the pressure accelerating it outward reaches atmospheric pressure.
The outward rushing air has inertia, the air moves outward reducing the pressure of the region of air which was inside the balloon.
The combination of surrounding atmospheric pressure ahead and lowered pressure behind slows down the outward flowing air, brings it to a stop and accelerates it back toward the region where the balloon was.
Once again inertia causes an overshoot and the pressure increases above atmospheric.
The pressure oscillates above and below atmospheric. The amplitude of the pressure oscillations decreases with time.

Slide a test tube brush through a narrow PVC or acrylic pipe.
When it reaches the far end it pops open just like the compressed air in a sound wave.

Consider a traveling sound wave moving through a tube. The sound wave is made of regions in which air has a pressure above atmospheric pressure and regions in which the air pressure is below atmospheric pressure. A high pressure region is called a compression while a low pressure region is called an expansion.
The compressed air is held in by the walls of the tube. A region of compressed air moves along the tube by compressing the air in front of itself.
When the compressed air reaches the end of the tube it can expand to the side.
The air in the compression accelerates outward gaining speed as long as it is above atmospheric pressure.
It reaches maximum speed outward as its pressure reaches atmospheric pressure.
The air continues outward carried forward by its own inertia reducing the pressure near the mouth of the tube to below atmospheric.
The resulting expansion propagates down the tube.

So the wave reflects off the open end, with a compression turning into an expansion.

It might help to recall a pendulum.
Pull a pendulum up to one side and let it go. Gravity pulls it down accelerating it until it reaches the bottom. At the bottom, there is no force accelerating the pendulum however it has maximum speed and its inertia carries it through the bottom. The pendulum overshoots the bottom of its swing going up, slowing down stopping and returning. It oscillates back and forth until its energy is dissipated by friction.

Bells on horns.

One role for the flared bell on the end of a trumpet is to allow the air to expand outward gradually. This decreases the overshoot of the oscillating air. Less energy reflects from the open end, so that more energy leaves the horn.
The horn is louder.

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 Scientific Explorations with Paul Doherty © 1999 7 June 2000