Sound waves: How do we know it is the fundamental harmonic?

[SweatingBear]

I have done a handful of problems related to sound waves in air columns and one thing I have noticed is that, unless told otherwise in the problem formulation, one always assumes that sound wave that is formed is always the fundamental harmonic and thus the length of the air column comprises a half wavelength. What is the rationale behind this? I thought the shapes were somewhat arbitrary, depening on the context: How is one so sure that it most certainly is the fundamental harmonic? Why couldn't the sound wave have e.g. a 2nd harmonic or a 3rd harmonic shape?

Example:

If you blow into a bottle with length 17 cm a standing wave arises. What is the frequency of the soundwave (assume the speed of sound to be 340 m/s).

In this case, the sound wave is regarded as a fundamental harmonic (read: must be regarded as the fundamental or else the answer turns out to be wrong). What argues for doing that?

Example:

In a straight tunnel, similar to an air column with both ends open, resonance is achieved at e.g. the frequency 42 Hz. The next frequency which gives rise to resonance is 56 Hz. Calculate the length of the tunnel.

In this example, one cannot assume that the shape of the sound wave is the "fundamental" (i.e. anti-nodes at the ends and node in the middle of the tunnel). Instead, one has to be quite careful and consider the possible shapes.

Can somebody please help me see things clearly?

 

[Nugatory]

The first harmonic is by far the easiest to excite, and it is usually quite difficult to excite any other harmonic by itself.

So unless you have some good reason to suspect otherwise, when you only find a single resonance you can reasonably assume that it's the fundamental harmonic; and when you find multiple resonances you can work out the fundamental harmonic.

In practice, you might find it fairly difficult to create the situation described in your second example in which just 42 Hz and 56 Hz are present but the 14 Hz primary is not there and dominating them both.

 

[SweatingBear]

The first harmonic is by far the easiest to excite, and it is usually quite difficult to excite any other harmonic by itself.

Ok, valid argument but how can really be sure that it really is the fundamental harmonic? Why couldn't one argue that it is the first harmonic?

In practice, you might find it fairly difficult to create the situation described in your second example in which just 42 Hz and 56 Hz are present but the 14 Hz primary is not there and dominating them both.

Hm, not sure whether I really understood the "14 Hz" bit. But, why can't I here assume it is the fundamental harmonic? Like you said, any higher harmonics are way harder to excite.

 

[technician]

The fundamental may have length of column = λ/4 (when one end is closed and the other is open)
From the dimensions of the container you should have some idea.
Also, negatory is quite correct, the fundamental is the most likely oscillation to be excited

 

[sophiecentaur]

The best way to ascertain that you are near the fundamental resonance is by measuring the dimensions of the pipe. You will not get a resonance in a simple pipe or cavity if the dimension is much less than a quarter wavelength in air. If the resonator is loaded in some way, with a port (hole / tube) in it then it can behave as a Helmoltz resonator at a much lower frequency (like a sub-woofer loudspeaker).
For a 'black box' resonator (no data about its real dimensions), you would need actually to measure its response down to a ridiculously low frequency, to be really sure, I think.

 

[0xDEADBEEF]

You can get to the higher harmonics by blowing harder with many flutes, but it requires some skill. http://en.wikipedia.org/wiki/Overblowing Large harmonics usually have higher power dissipation, so they are harder to excite, it is often a save bet to assume that you are in the fundamental resonance. If you have something else than simple pipes, the vibrational patterns get much more complicated, and the harmonics don't necessarily follow a simple pattern of multiples of a single base frequency. http://en.wikipedia.org/wiki/Ernst_Chladni

 

[sophiecentaur]

You can get to the higher harmonics by blowing harder with many flutes, but it requires some skill. http://en.wikipedia.org/wiki/Overblowing Large harmonics usually have higher power dissipation, so they are harder to excite, it is often a save bet to assume that you are in the fundamental resonance. If you have something else than simple pipes, the vibrational patterns get much more complicated, and the harmonics don't necessarily follow a simple pattern of multiples of a single base frequency. http://en.wikipedia.org/wiki/Ernst_Chladni

That's because they are 'overtones' and not 'harmonics'. It's only a harmonic when it is an exact multiple of a fundamental and, for most resonators (real ones) this is not the case. I always think that the right terminology should be used where possible.