Background
I am driving a cheapo 8 Ohm speaker with an LM386. The LM386 circuit is nearly identical to the one in the datasheet shown below, except Vin is AC coupled through a 10uF capacitor and the 250uF capacitor is only 100uF. The speaker looks similar to the one in the digikey link below, but I am not sure about the exact model.
https://www.digikey.com/product-detail/en/pui-audio-inc/AS03608MR-5-R/668-1398-ND/4147322
I am connecting the input of the LM386 to a function generator and driving it with a sine wave. Then, I am using a near field E-field probe to measure the electric field next to the speaker. My E-field probe is the broadband one in the kit linked below.
https://www.com-power.com/ps-400_near_field_probes.html
At the resonant frequency of the speaker (~510Hz), I am able to measure about 10mV pk-pk sine with the E-field probe right in front of the speaker diaphragm. The amplitude decreases when the probe moves away from the center of the diaphragm. The signal becomes very small or unmeasurable at other frequencies.
When the E-field probe is in front of the center of the diaphragm, the measured E-field is 180 degrees out of phase with the LM386 output. If I move the E-field probe to center of the back of the speaker, the measured E-field is smaller and it is also in phase with the LM386 output. Swapping the speaker leads maintains the 180 degree phase difference between the field measured in front of the diaphragm and behind the speaker, but the phase relative to the LM386 output is reversed.
Opening up the speaker and looking at the voice coil, the wire wraps down and then wraps back up on the outside. The result is that both ends of the wire are at the same end of the coil and there are 2 concentric cylinders of wire.
As a side note, I am not able to measure anything with the H-field probe. Neither at the center of the diaphragm nor along the wires connecting to the speaker. I realize the bandwidth of the probe is much higher frequency and it may not be sensitive enough.
Question
How is the speaker radiating E-field? Why is it only happening at the resonant frequency? Why is the phase different between the front and back of the speaker?
Thank you!
EDIT: After opening up the speaker I found that the voice coil is wound in a way that the two ends of the wire end up on the same side. This may disprove the hypothesis that there are opposite charges on opposite sides of the coil.
I am not sure about this answer. Please correct me if it is wrong. I thought of this answer with the help of @Dave Tweed's answer.
The speaker is radiating E-field because it has charges on opposite ends of the voice coil that are moving.
The field is at a maximum at the resonant frequency because the peak velocity of the voice coil is at a maximum. Though the amount of peak charge is proportional to the peak voltage and is constant, the higher the peak velocity of the voice coil the greater the rate of change of the current density and the greater the electric field.
The field has opposite phase on opposite sides of the speaker because it is dominated by the field from the nearest charge, and the opposite sides of the coil have opposite charges.
The analysis for these answers is shown below.
The voice coil has a sinusoidal motion at resonance with position \$x\$, velocity \$x'\$, and acceleration \$x''\$. The force on the coil is proportional to both the current and the acceleration, so the current and acceleration are in phase. The voltage is equal to the current multiplied by the coil inductance, because at resonance the reactive part of the mechanical system is zero. The voltage has a 90 degree phase lead relative to the current and the acceleration, so it is in phase with the velocity of the voice coil. The charge on the voice coil is also proportional to the voltage and is in phase with the velocity.
The curl of the magnetic field is equal to the current density which is proportional to the charge multiplied by the velocity. Since the charge and the velocity are in phase, the current density is proportional to \$cos^2(t)\$. The curl of the electric field is proportional to the negative of the time derivative of the magnetic field and is proportional to \$-cos(t)\$
The greater the time derivative of the current density the greater the electric field. Since the amplifier has low output impedance, the voltage across the coil is constant and the charge is constant. Only the velocity of the coil can be increased to increase the time derivative of the current density. The velocity of the coil is maximum at the resonant frequency.
Best Answer
The metal case should give you lots of shielding. And the e-field should all be coming from the solder terminals and the coil-wires on the cone.
Since this doesn't appear to be the case, then probably your speaker has a plastic cone. If the plastic has been touched by fingers, or worse, rubbed against a plastic bag, or against clothing, then the plastic may still have a significant surface-charge of several hundred volts wrt earth. (How low is the humidity at your workbench?!)
Plastic typically charges negative when touched by human skin, so the moving speaker would produce a negative peak when it physically moves towards the e-field sensor. Also, as the charged speaker-cone moves in and out, it would produce a strong opposite charge on the metal frame, caused by electrostatic induction (as if the speaker cone is a vibrating capacitor plate, and the metal frame a second capacitor plate.)
Try holding the vibrating cone with fingers, to see if the large signal disappears when AC is applied yet the speaker cone doesn't move. If an electrostatically-charged plastic plate is vibrating, it will produce a strong AC e-field easily detected by nearby electrode-antennas.
To get rid of any surface-charging, perhaps use a slightly-damp bit of toweling to wipe down the entire plastic speaker surface. If after discharging the plastic, your strong signal is smaller (or even missing,) then the cause was a charged-up speaker cone, rather than the AC drive voltage. Or instead, before wetting it, try rubbing the speaker cone with a plastic sheet, a rubber balloon, or arm-hair. If this makes your e-field signal enormous, then you've found the most probable cause. (And in that case, also try rubbing it with plumber's teflon tape, or with a plastic bag, with rubber, paper, etc. Check for different polarity of sensed pulses!)
Also, using a vibrating or rotating surface is a classic way to create a "Field Mill" for detecting any e-fields which have no AC component. Your near-field probes can only detect the changes in fields, not the fields themselves. Attach a small disk of foil to your vibrating speaker, connect it to an AC dvm or scope-input using thin foil strip, then vibrate the speaker. See if you can use this Field Mill to detect a distant hunk of styrofoam which you've rubbed on your hair.
https://www.google.com/search?q=diy+field-mill
Also, you can sense a charged plastic speaker-cone by waving the gate-lead of a JFET/LED circuit near it, as with http://amasci.com/emotor/chargdet.html