Why is the amplitude maximum at the open end of a closed and open end tube?

[cks]

Consider a scenario of a sound wave inside a closed end and opened end tube.

We always learn that the displacement amplitude at the closed end is always zero but at the opened end is always maximum.

My friend can see it quite intuitively.

For the closed end, we expect there is no motion of air. So, the amplitude is zero.

But I don't find it intuitive to imagine how the amplitude at the open end is of maximum?

Thank you.

 

[tiny-tim]

Consider a scenario of a sound wave inside a closed end and opened end tube.
…
For the closed end, we expect there is no motion of air. So, the amplitude is zero.

But I don't find it intuitive to imagine how the amplitude at the open end is of maximum?

Hi cks!

Sound is a traveling longtudinal pressure difference.

A sound wave in a pipe is a standing wave, and therefore cannot exist unless there is reflection at both ends.

First consider single a pulse (not a wave).

At a closed end, a pulse of high pressure is reflected as a pulse of high pressure.

At an open end, a pulse of high pressure is reflected as a pulse of low pressure (and vice versa) … a 180º "change in phase".

This is because when the high pressure pulse leaves the pipe, it spreads out spherically, rapidly becoming atmospheric pressure, and suction is created behind it.

In other words, there is a reduction in pressure behind it, and this low pressure will pulse back down the pipe.

It is this sudden reduction in pressure cause by the ability of the wave to spread out which makes the difference.

That's fairly clear for a single pulse, though not so clear for a wave, but the principle is the same.

For a lot of detail, including a rather good animation, see this Australian site: http://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html#time

(Another way of looking at it is that the open end of the pipe is at high pressure, and the air beyond it is at ordinary pressure, so it behaves like a boundary between two fluids of different pressure, and so a reflection is to be expected. )

 

[cks]

Thanks for your answer. It's quite clear and straightforward.