Why is the open end of a tube a node for a standing wave?

[kostoglotov]

I understand, from my textbook, that certain frequencies of sound (depending on the length of the tube) will reflect off the interface between the air in the tube and the air outside, that this interface is a discontinuity.

But in all other cases where discontinuities caused (partial) reflections of waves (such as in two different strings with different linear densities at the same tension), the reflection was associated (I thought attributed to) the change in velocity of the wave across the mediums.

But the air in the tube is the same as the air outside the tube. Shouldn't the speed of sound waves be the same for the outside air and the air inside the tube? Why is the open end of the tube a discontinuity for sound waves?

 

[ehild]

I understand, from my textbook, that certain frequencies of sound (depending on the length of the tube) will reflect off the interface between the air in the tube and the air outside, that this interface is a discontinuity.

But in all other cases where discontinuities caused (partial) reflections of waves (such as in two different strings with different linear densities at the same tension), the reflection was associated (I thought attributed to) the change in velocity of the wave across the mediums.

But the air in the tube is the same as the air outside the tube. Shouldn't the speed of sound waves be the same for the outside air and the air inside the tube? Why is the open end of the tube a discontinuity for sound waves?

The reflection is determined by the acoustic impedance. It is not the same for the air in the tube as the air in the free space. So there is reflection even at open end.
Sound is a pressure wave. At the open end, the pressure is he same both inside and outside of the tube, The pressure variation is zero: it is a node of the sound wave.