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LM386 Hearing Aid Circuit needs improvement.

If I could find a graph of a real trumpet radius I could copy it very close.
The ideal shape has an exponential taper.
 
The ideal shape has an exponential taper.

Which one? Slow or fast?

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This is what you call, research and development.
It has been mentioned that not being able to hear birds etc is a higher frequency hearing issue, so the correct shape will amplify higher frequencies, horn shapes will attenuate higher frequencies.
Amplifying the correct frequencies for your requirements will take some R & D.

 
The real horn shape is finished, I copied the fast delay curve on the graph. I made 1 part then traced around it to make 3 more parts then taped all 4 pieces together. Very first thing I notice the real horn shape hums, the other horn shape does not hum. I swapped the mic back and forth from each horn several times the first horn I made has no hum at all. Why would the real horn shape make the amp hum? I tested the new horn I can not tell it works better or worse than the other horn. There is no high frequency with either horn but I can hear to talk to people. The tiny amp need frequency adjustments. Both horns are 6' x 6' square the 1" square tube is 8" long on both horns. I just learned if I hold my finger as close to the cardboard horn as I can but don't touch the cardboard hum stops. ???

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Why would the real horn shape make the amp hum?
It may be more efficient, two things that may be worth trying is to taper the parallel section.
It appears you have a closed end with the mic in it, try an open end with the mic positioned in it.
This may have something to do with it?
Search for
Khan Academy "Introduction to sound review"

 
It may be more efficient, two things that may be worth trying is to taper the parallel section.
It appears you have a closed end with the mic in it, try an open end with the mic positioned in it.
This may have something to do with it?
Search for
Khan Academy "Introduction to sound review"


24 hours later amp is not making hum sound anymore. That is strange could it be 24 hours later wet glue has become dry and that reduced the hum sound? I can push the mic to any location inside the 8" long square tube. I read the physics of a closed tube vs an open tube sound will be much louder in a closed tube that must be why I don't need 200 amplification volume control 3% to 10% is all I need to get an excellent loud signal. My ears hear no high frequency below 60 db this amp needs equalization a tone control knob for every 1K frequency range or only the high Khz range.

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Please think about covering the connections of your lithium battery assembly. There is a huge amount of energy stored in those and one careless move could set them ablaze.
 
Please think about covering the connections of your lithium battery assembly. There is a huge amount of energy stored in those and one careless move could set them ablaze.
I know lithium batteries are dangerous if they get shorted. I need to buy a battery holder for 3 batteries and some solder in place fuses. My wires are #24 plus I have an on/off switch soldered between the batteries. With switch off wires can't short out.
 
I built another new cardboard horn the correct design and tested it. Soon as I move 2 ft away from my laptop computer 60 Hz hum is gone. I adjusted the volume and had no trouble talking to my wife. Sound seem to be more clear than the other horns that I tested. Volume knob is not up very much maybe 5%. Horn is 5" square 11½" long. There is no feedback. This is a very interesting project, it works much better than the Big Ear project I built 50 years ago. I am amazed that I can hear anyone I can see and understand what is being said.

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This may assist in enhancing some higher harmonics.

Explain how waves interfere in a closed pipe.​

In a closed pipe, waves interfere by creating standing waves through the superposition of incident and reflected waves.

In more detail, when a wave is produced in a closed pipe, it travels down the pipe and upon reaching the closed end, it is reflected back. This reflected wave then travels back along the pipe and meets the next incident wave. This meeting of the incident and reflected waves is what we call interference. The type of interference that occurs depends on the phase difference between the two waves. If the waves meet in phase, constructive interference occurs, leading to an increase in amplitude. If they meet out of phase, destructive interference occurs, resulting in a decrease in amplitude or even cancellation of the wave.

The interference of waves in a closed pipe leads to the formation of standing waves. Standing waves are characterized by nodes and antinodes. Nodes are points of complete destructive interference where the displacement of the medium is always zero. Antinodes, on the other hand, are points of maximum displacement resulting from constructive interference. In a closed pipe, there is always a node at the closed end and an antinode at the open end.

The fundamental frequency, or first harmonic, of a closed pipe is when there is only one node-antinode pair along the length of the pipe. This occurs when the length of the pipe is equal to a quarter of the wavelength of the wave. Higher harmonics, or overtones, occur when there are multiple node-antinode pairs along the pipe. These correspond to frequencies that are odd multiples of the fundamental frequency.
 

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