Open-ended pipe
Many interesting problems in acoustics involve the radiation of sound from the end of a pipe. These range from the noise produce by car exhausts to the acoustics of wind instruments like flutes or organ pipes.
In your physics lessons you will have seen how open-ended pipes have resonances, similar to strings, but with antinodes of particle displacement at the open end. These correspond to pressure nodes. At low frequencies, where the wavelength is long compared to the diameter of the pipe, this is a very good approximation as you can see from the first animation below, where one end of such a pipe is shown. The pressure patterns alternate between high and low pressure, as we would expect from a standing wave. The pressure node, however, is not exactly at the open end, but a little way beyond. Not much sound escapes from the end of the pipe.
When the wavelength is shorter, and comparable with the diameter of the pipe this effect is much more pronounced, the pressure node is even further from the end of the pipe, and the sound is radiated much more efficiently.
