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Re: [Phys-L] Resonance with tuning forks vs small speakers



On 10/28/22 12:03 PM, Zeke Kossover via Phys-l wrote:

As a resonance activity, I bring a vibrating tuning fork towards a tube
that is open at one end and closed at the other. When tuned correctly, the
air in the tube loudly resonates.

Since tuning forks are expensive and every student has a phone with a
speaker, I've tried running the activity with a frequency generated by
their phone. To my ears, the sound generated by their phones is way louder
than the tuning fork, but when I put the phone next to the tube, the
amplitude increase is way less.

I wonder why they are so different. Do any of y'all have ideas?

1) The short answer is I don't know.

2) Here's a possibility. It is an easily-checkable hypothesis.

Consider formulating the issue in terms of impedance matching
and acoustic transformers.

An electrical transformer with a big turns ratio can be used to
convert a high-voltage low-current signal into a low-voltage
high-current signal. That means there is a drastic change in
the impedance.

Now consider the acoustical analog. The tuning fork moves a
small amount of air with an almost unstoppable force. Massive
metal versus squishy air. You would get a louder noise if
you could move a larger amount of air, and a not-so-unstoppable
force would still be enough.

*) A loudspeaker typically has a lightweight cone that serves
as an acoustic transformer between the massive voice coil and
the squishy air.
*) The ones that don't use a cone use a tapered horn, which is
another way of making an acoustic transformer.
*) A resonance is another way of monkeying with the impedance.
Loudspeakers don't do it this way, because it only works at
one frequency, but it does work. At resonance, the inductive
iωL impedance cancels the capacitive 1/iωC impedance, and
you can then couple to whatever minor resistive impedance
remains.

The phone doesn't have have an impedance problem because
the problem has already been solved by skillful engineering.
That is, the phone has nothing to gain by further transformer
action, because it is already lovingly impedance-matched to
the air.

You can test this hypothesis by playing with various means
of impedance-matching the tuning fork to the air. Perhaps
the cleanest way is to make a horn. An exponential horn is
best, but a cone is good enough. There is a small opening
at one end and a large opening at the other end. Another
name for this is megaphone. Hold one tine of the tuning
fork near the small end. I predict a marked increase in
radiated sound energy.

A simpler scheme for impedance matching would be to glue
a small stiff radiator to one tine of the tuning fork.
Something the size of a postage stamp should be enough
to produce a marked increase in radiated sound energy.

If you happen to have a violin lying around, you can
touch the foot of the tuning fork to the body of the
violin. That's a well-engineered acoustic transformer.

3) Partially related and partially not: The two tines
of the tuning for vibrate in opposite directions. This
is a disaster in terms of radiated power. All the more
so because they are separated by much less than one
wavelength. Horrendous cancellation of the radiated
field. Anything that breaks the symmetry will improve
the coupling to the radiated field. Depending on the
geometry, your resonator might be helping you with
this. The transformers mentioned in section (2) are
designed to brutally break the symmetry.

4) These are my off-the-cuff thoughts. It is entirely
possible that I am missing some important physics here.
See item (1).