Wired headphones to a cellphone, (like wired speakers to a stereo player) get the electric signal from the cable in an analog way, it contains both the energy and the signal.

That is enough to move the magnet&membranes in the speaker and reproduce the sound.

But for wireless speakers, the wireless signal does not transfert [enough] energy. And the headphone needs a source of electric power to : run the Bluetooth receiver/sender, and move the membrane to produce the sound.

[Edited to add remark]

Wired ones are drawing power from the phone to work, wireless ones draw power from the battery inside the wireless buds themselves, when the wired earbuds are plugged in, that’s the only time you could use it, because that’s the only time it can draw power, it doesn’t matter if it’s not from a charger port, the charger port is where the phone gets its own power from

Oh boy. This is a fun rabbit hole.

Tl;dr: the sound waves from the music are converted to electrical waves and sent to the headphones down the cord to the speakers in the ear buds.

The longer version -

Do you understand how a speaker works? There are magnets in speakers. The magnets are connected to the speaker cone.

When an electrical signal is sent to the speaker, the electrical signal goes to a coil in near the magnet.

Now remember, magnets have north and south poles - Positive and Negative. When the electrical signal goes through a wire it creates an invisible electrical field. This electrical field, depending on the orientation, will attract or repel the magnet.

The magnet is attached to the speaker cone. Instead of the coil of wire moving, the magnet and the speaker cone moves. This causes vibrations in the air that we hear with our ears.

So when you put a sound wave as an electrical signal into the wire it will cause the speaker to move.

Here's an example video illustrating how it works. https://youtu.be/CN6lmC6bgxE

When you have air pods or wireless ear buds, in order to generate the electrical signal to move the magnet you need some sort of power.

FUN FACT: Did you know that a speaker could also be used as a microphone? It may take a lot of yelling to move the speaker cone, but it can be done. The air waves would move the speaker which moves the magnet in the coil. That magnet moving in the coil of wire induces electrical current inside the coil and creates an electrical signal.

Audio files, streaming services, etc, basically transfers audio in a digital format. The digital format is then used to reconstruct an analog electrical signal, which is then sent to a speaker to convert into vibrations (using magnets) that we can listen. That is the basic of how audio works.

Sending audio through a headphone jack means, your phone/laptop/media player first converts the digital audio file/stream into the analog electrical signal, and then amplifies this signal to a certain level, before sending the result out using the headphone jack to the earphones/headphones. How loud the sound coming out from your earphones/speakers, depends on the amplification of this electrical signal. For commercial earphones and headphones, the amplification needed is not that much, and so phones/media players are able to internally amplify the electrical signal, and send it to the headphones/earphones, at the cost of its own batteries. Old headphones uses slightly different magnets such that it needs more amplification for it to work properly, and so they have their own power supply to amplify the audio electrical signal before sending to the magnets to produce vibrations.

When it comes to speakers, where you'll need it to be louder than earphones/headphones, the amplification required is larger, so more power is needed to amplify the electrical signal. Some speakers have built in amplifiers - basically if you see a speaker that is connected to a power source / uses battery, it has a built in amplifier. Even if the power source is a USB cable connected to your laptop/computer, that is still an in-built amplification - and others will require an external amplifier, but key point is, for an electrical signal to be heard, an amplification is needed.

When it comes to wireless technology, audio signal from the phone is sent through digital wireless communication, most commonly used being Bluetooth. So, the conversion from digital to analog electrical signal, happens on the wireless headphone itself. After that, again the electrical signal needs to be amplified to a certain level that it is audible, and that is why the wireless headphone needs its own batteries/power source. First, to power the digital to analog converter (DAC), and then to amplify this analog electrical signal.

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Headphones are basically tiny speakers. A speaker works by having electric current vibrate a magnet attached to a diaphragm, and these vibrations are the sound you hear. In wired headphones the electric current goes straight from the device to the magnet over the wire. With wireless, the headphones are basically little computers with a tiny Bluetooth chip. The device sends a digital signal which the Bluetooth chip receives. Then the chip translates this into the current that drives the magnet. So the chip needs battery power to operate the tiny computer and generate the current. But with wired, since the current is coming over the wire and there’s no tiny computer to power, no charging is needed.

Because they're taking power from the phone through the headphone port.

Speakers that take external power do so because the headphone port can only supply a certain amount of power.

The technology behind wired and wireless headphones is very different. Wired headphones use a cable to connect to your phone, which uses very little power. Wireless headphones use Bluetooth, which uses more power and therefore needs to be charged more often.

The power goes through the wire.

If you've ever had noise canceling wires headphones, they need to be charged because the wire power is just enough for the speakers and nothing else

Same for computer speakers. Used to have some that just needed the 3.5mm audio jack. Others need usb. And the powerful ones need to be plugged into the wall.