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The Usual Answers and Responses:

Encoding, Compression, and Buffering

The typical answer to this on the internet is because Bluetooth headphones require the conversion of one form of data information into another, and the time it takes to do this is what causes the delay (see SoundCore PocketNow or How to Geek). Bluetooth has to take a digital signal that is compressed, they say, send it through the air to your headphones, where it is then turned into an analog signal, and then blasted out the little speakers in the headphones. This leaves some questions.

For example, why do wired headphones not require similar buffering? I would think the answer to that would be because they keep the signal analog from start to finish, but how does that make sense on DIGITAL computers? At some point, you are going to have to take that binary code that makes up videos and audio and convert it into analog to be used by the headphones. With wired headphones you convert the digital to the analog at the beginning whereas with Bluetooth, you send a digital signal and it's turned into analog at the end. I guess the difference in speed is because with wired headphones the more powerful processor is doing the conversion, i.e. the phone or computer versus the headphones. Is this correct?

Impossible to transmit analog data wirelessly?

Further, I have read in several places (for example, the PocketNow website I linked above) that the raw data cannot be sent wirelessly, but you can do a simple Google search for "wireless analog transmitter and receiver" and you will find plenty of options. For example: Applied Wireless, Define Instruments, Imagine Industrial Controls, Abacom-Tech, and there are many more. I did notice that all of those devices are much bigger than would be required for headphones, but I believe their size has a little to do with their range, so I think you could miniaturize the heck out of these things if you only needed 25 or so meters of range (but I am open to correction on that.)

Signal transmission velocity

Copper:

Then there's the speed of light through a medium. According to the BBC, signals propagate through copper at around \$0.9c\$ or \$2.7 \times 10^8 meters/second\$ where \$c=\$ speed of light in a vacuum.

Air:

It was surprisingly difficult for me to find an actual number regarding how fast a signal propagates through air, and maybe that is because it is virtually unchanged from a vacuum. According to Libre Texts, the speed of electromagnetic radiation, Bluetooth specifically included, is "\$3 \times 10^8 m/s\$" or roughly \$1.001c\$. Since we know nothing can go faster than \$c\$, exactly \$=299,792,458 m/s\$ it is safe to say Libre Texts is rounding up. NOAA does the same rounding. This left me to attempt the problem on my own.

According to Lumen Learning (among other places, and here) the refractive index of air is approximately \$1.000 293\$.

I believe the speed of light in a medium is given by:

$$v = \frac{c}{n}$$

where:

  • \$v\$ is the speed of light in the medium,
  • \$c\$ is the speed of light in a vacuum (\$299,792,458 \text {meters per second}\$),
  • \$n\$ is the refractive index of the medium.

Substituting the values:

\$v = \frac{299,792,458 \text{ m/s}}{1.000 293}\$

Calculate to get the speed of light in air in \$meters/second\$:

$$v = \frac{299,792,458}{1.000 293}$$

$$v \approx 299,704,644.539 36 \text{ m/s}$$

Next, the \$c\$ value:

$$c = \frac{299,704,644.539 36}{299,792,458}$$

Speed of light through air: $$c \approx 0.9997077$$

Difference in transmission speed through versus copper

This means that the signal through the air moves ≈9.97% faster than the signal through the cable.

The Question:

If both wired and unwired headphones have to convert a digital signal to an analog signal at some point, and it is possible to send analog signals wirelessly, lastly, signals travel faster through the air wirelessly than wired through a copper cable, why do Bluetooth headphones have a longer delay than wired headphones?

If the answer has something to do with compression and conversion, please explain specifically why the wired headphones are able to bypass these formatting problems. As a sort of bonus question, is the delay specific to Bluetooth? For example, could some other format of wireless transmission beat wired transmission, or will it always be the case that wired headphones will have less of a delay than wireless?

One last minor note. It dawned on me at the last moment that, due to the compression/buffering/Bluetooth that this question might belong on the Computer Science Stack Exchange, so let me know what you think regarding that.

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  • \$\begingroup\$ You've got several good answers to your questions. You might be interested in looking at the "in-ear monitors" used by musicians in live performance where the Bluetooth delay would be unacceptable. I haven't studied the topic. \$\endgroup\$
    – Transistor
    Commented May 12 at 13:16

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Why is there a greater lag in Bluetooth headphones compared to wired?

It's got nothing to do with transmission speed AND, it's got everything to do with signal integrity. A signal transmitted using low power Bluetooth radio is subject to all sorts of interference, glitches and fading so, if you tried to reconstruct the signal the instant it arrived, the music playing in your headphones would be full of glitches and nastiness.

On the other hand, if you allowed for packets to be received and retransmitted (on request) if deemed to be faulty by the error checking mechanism then, given sufficient delay and buffering, you can reconstruct the analogue signal and avoid the instantaneous packet retransmissions that are mainly always needed.

This is why Bluetooth must be delayed.

It's a bit like playing a YouTube video over a poor data rate connection. Better to let it stream (on pause) for a while then hit the play button.

Copper delivers a very, very high signal integrity and doesn't suffer from moderate interference at all. No such thing as fading or other "systems" sharing the same medium (the copper wire) hence, no delay is needed.

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    \$\begingroup\$ That makes PERFECT sense, now. I didn't think of interference. Thank you! \$\endgroup\$ Commented May 12 at 11:21
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    \$\begingroup\$ Buffering for transmission errors is only one part of the delay. Even in perfect conditions, the audio compression and decompression algorithms will be the major limitation you can't get away with. \$\endgroup\$
    – Justme
    Commented May 12 at 12:14
  • \$\begingroup\$ As an example of what happens in unbuffered wireless audio, consider analog radio stations that become increasingly unclear when you move away from the station. But these stations still typically have lower delay than Bluetooth despite being dozens of km away. @CuriousLayman \$\endgroup\$
    – tobalt
    Commented May 12 at 16:41
  • \$\begingroup\$ nitpick: In the last sentence, you should say copper cable instead of wire. Using an actual single copper wire (telegraph ing) does make it a shared medium with other single wires using the same return and fields in between. \$\endgroup\$
    – tobalt
    Commented May 12 at 16:46
  • \$\begingroup\$ @Justme And, the reason for that compression and decompression is to make it so that you don't need as many packets to reconstruct the full signal? \$\endgroup\$ Commented May 18 at 5:16
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The difference between plugging in the phones to analog output and over Bluetooth is really about the things you said.

If you simply plug in to analog output, the computer audio interface IC streams the digital audio to DAC which converts the audio to analog signal that is sent out over wires to speakers. The DAC itself has very small pipeline to process the audio, so the audio comes out after a delay of few or few ten samples - less than a millisecond.

Where Bluetooth fits in is kind of between the audio interface chip and the DAC.

The audio compression algorithms to compress the audio to low enough bandwidth to fit through the Bluetooth link happens like many other audio compression algorithms, they happen in blocks, just like AAC or MP3.

You first need to receive a full block of audio samples. While running the compression algorithm on the first block, you are already receiving the second block of audio samples. When transmitting the first compressed block out over Bluetooth, you are compressing the second block, and receiving the third block from audio interface IC.

If the block size is 10ms, you first need 10ms delay to receive the block, 10ms to compress it, and 10ms to transmit it out.

On the Bluetooth receiver, you need to receive compressed 10ms block, then use 10ms to decompress it, and then play the decompressed audio for 10ms.

Then add a suitable amount of buffering and caching to tolerate transmission errors and resending the dropped data packets, you already have several 10s of milliseconds delay before you have the digital uncompressed stream you can send to DAC for converting the signal back to analog and send to speaker.

So no, the delay is not specific to Bluetooth. Same thing must happen when compressing audio to fit through any interface.

And yes, you can send analog audio wirelessly. Such headsets are commonly sold and can be bought from almost any store that sells headphones, although they might have benefited from digitalization of that technology too. Some of them used infrared light and some of them use radio transmission to transfer the audio. You are not limited to wired or Bluetooth headphones.

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Most of this discussion is a red herring since when you are watching a video, the system knows about the latency of bluetooth and offsets the video and audio streams accordingly. You don't get to experience a difference.

It is only in interactive applications (gaming, playing music together on the Internet, monitoring while recording) that there is no way to compensate for latency.

Now analog/digital conversion and back takes time: not as much the conversion as such but the antialiasing filtering that is necessary to remove sound artifacts. Higher oversampling ratios help, and particularly sample rate overkill helps: if you are transmitting at 44.1kHz sample rate, the antialiasing filters cutting off everything at 22.05kHz at the latest need to be very steep if they are supposed to support transmitting signal components at, say 19kHz. Steep filters have long responses and you need to wait for the response to abate before sampling the rate-reduced signal.

The same is the case for the D/A conversion at the end of the pipeline.

Now Bluetooth is compressed and packeted. Compression needs lookahead, packeting introduces delays by protocol overheads and retransmission as needed.

That dwarfs the conversion delays.

Wirelessness does not come into play at the distances in question since the transmission itself is essentially instantaneous. As a result, you can use FM headphones (using analog transmission techniques) essentially without any latency or delay at the price of a reduction in dynamic range and in noise resilience.

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