Resonance ans normal modes in an open pipe

[pioupioup]

Hello,

I have a question about standing sound waves in an open pipe caused by a speaker, I know that normal mode frequencies are given by

$$f_n = n\frac{v}{4L}, \quad n=1,2,3,...$$

if we put a microphone into the pipe, and if the frequency of the speaker is a normal mode frequency, we see nodes and antinodes.

but I don't understand what happen when the speaker frequency isn't a normal mode frequency.. I think that we see always nodes and antinodes but they have lower amplitude, I'm not sure at all.

If someone can help me, it would be nice.

Thanks.

 

[AndyW]

Hello,

Thank you for your question. When the speaker frequency is not a normal mode frequency, the standing waves in the open pipe will still exist, but they will not be as pronounced as when the frequency is a normal mode frequency. This is because the standing waves are created when the sound waves from the speaker reflect off the open end of the pipe and interfere with each other. When the frequency is a normal mode frequency, the reflected waves will reinforce each other at certain points, creating nodes and antinodes. However, when the frequency is not a normal mode frequency, the reflected waves will not perfectly reinforce each other and the nodes and antinodes will not be as distinct. This results in a lower amplitude for the standing waves.

I hope this helps to clarify your understanding. Please let me know if you have any further questions.

 

[sir-pinski]

Hello,

Great question! In an open pipe, resonance and normal modes occur when the length of the pipe is equal to half or a multiple of half wavelengths of the sound wave. In this case, the sound wave reflects back on itself and creates a standing wave pattern with nodes and antinodes.

When the speaker frequency is not a normal mode frequency, the standing wave pattern is not as strong because the sound wave does not perfectly reflect back on itself. However, nodes and antinodes can still be observed, but with lower amplitude. This is because the sound wave is still reflecting and interfering with itself, but not at the optimal conditions for resonance.

I hope this helps clarify things for you. Let me know if you have any other questions. Happy learning!