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I see many 1/4 TS 'instrument' cables for sale with no mention of impedance.

With:

  • the speed of light in vacuum of ~300 000 km/s
  • audio frequencies < 20 kHz

you get wavelengths of at least 15 km(!). (Don't forget the velocity factor!)

It seems that for the case of a high-impedance output (guitar) into a high-impedance input (amplifier), transmission line effects and thus the impedance of an instrument cable is negligible. Is this correct? What about the frequency response of those cables?

And what about connecting low impedance (<0.5 kOhm) inputs/outputs together? Example: guitar amplifier head and cabinets? Can I still use 'instrument' cables for that purpose or does cable impedance start mattering in those cases?

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You've correctly analysed why the cable impedance does not matter in the way it does for HF transmission lines. (Though, the assumption of vacuum light speed is actually not completely valid – the dielectric factors into this, but it doesn't change the fact that the wavelengths are many times longer than any guitar cable.)

That notwithstanding though, the capacitance of that cable does have an impact on the sound – quite a lot in fact. Not for being part of the impedance as it matters for HF wave effects, but because electric guitars use high-impedance inductive pickups. This inductance forms with the cable capacitance a 2nd-order low-pass filter, whose resonance and cutoff frequency scales proportionally to the inverse square root of the cable capacitance. Thus a cable with low capacitance gives a brighter, twangier sound. (Only applies to passive guitars and basses.)

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  • You say that there's non-negligible 'capacitance' but the impedance is negligible? How can that be? A component's capacitance affects its reactance/impedance. So the impedance is not negligible afterall? (VERY interesting how the pickups couple with the cable capacitance. Never thought of it that way!)
    – Xunie
    Jun 29, 2020 at 16:41
  • @Xunie the impedance is a complex, the real part of it (resistance) can be negligible whereas the imaginary part (inductance) is not ;). The inductance will affect the phase of the wave...
    – Tom
    Jun 29, 2020 at 17:03
  • @Tom_C Capacitance is reactance. Together, the reactance and resistance of a component are considered its "impedance". How can the impedance be negligible if the capacitance (reactance) is not?
    – Xunie
    Jun 29, 2020 at 17:06
  • @Xunie I said "resistance" not reactance. A complex has a real and an imaginary part. The two of them do not have any reason to be linked.
    – Tom
    Jun 29, 2020 at 17:10
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    @Xunie yeah, my answer was formulated misleadingly. Capacitance is indeed part of impedance. I edited.
    – leftaroundabout
    Jun 29, 2020 at 18:13

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