#### xnor

##### Headphoneus Supremus

- Joined
- May 28, 2009

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some days ago I tried to calculate the resistivity of wires to determine the possible influence on the sound. Also did a comparison between copper / silver. I'm not sure if everything's correct but I'd say it is from taking a look at the results.

Stranded copper has a resistivity of 0.0178 ohm mm² / m and

silver's a bit lower/better: 0.0159 ohm mm² / m.

(based on the values from the CRC Handbook of Chemistry and Physics / Wikipedia)

AWG 24 wire has a diameter of 0.511 mm and cross-area of 0.205 mm².

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AWG 24 stranded copper wire has a resistivity of 0.086962431 ohm / m.

AWG 24 stranded silver wire has a resistivity of 0.077679925 ohm / m.

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Resistivity can have a big influence on the sound because speakers don't have a flat impedance. In fact speaker impedance changes with frequency. For example if you add resistors between your hp-out and headphones, you'll most likely hear a 'bass boost' and probably also some increased treble depending on the model. (see HeadRoom impedance charts)

For the calculations I took the following extreme values:

low: 32->64 ohm (e.g. PX 100) and

high: 320->640 ohm (e.g. HD 800).

Because the per-meter values were so low, I decided to calculate the maximum wire length up to the point where the wire resistivity could, in the worst case, lead to a change (voltage drop) of max 0.1 dB. (I don't know if this translates directly into SPL, but if it does it's inaudible.)

Keep in mind that many headphones have a much 'flatter' impedance curve, thus showing even much better results.

Results:

AWG 24

copper low: 8.6 meters / 28.2 feet

copper high: 86 meters / 282 feet

silver low: 9.6 meters / 31.5 feet

silver high: 96 meters / 315 feet

The difference between copper and silver is minimal (about 0.01 dB).

At those lengths the wire resistivity is about 2.3% of the speaker nominal impedance (Wikipedia recommends less than 5%, which would be about 0.2 dB).

Theoretically:

Using a 1 meter cable (copper), wires up to AWG 32 (0.2 mm diameter) could be used for the low ohm model and up to AWG 42 (0.06 mm diameter) for the high ohm model (based on their resistivity only!).

For 15 meters, low impedance AWG 22 should about do it, AWG 30 for high impedance.

For 30 meters: AWG 19 and 28 respectively.

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Hope there are no severe mistakes. Hope it's useful for someone.