Look at the Martin Logan spec above: they (each speaker) produce 89dB (Decibels, sound level) at 2.83V (volts) measured at 1meter away from the speaker, on-axis (straight in front).
So what this shows you is that voltage is sound level, a direct relationship.
Your volume knob setting is amplification, which is voltage output, So the same amplifier, set at the same volume knob level (lets say for illustration purposes the 9:00 position is 2.83V output which is the abovementioned 89dB) should give you the same amplification and same voltage output regardless of the speaker load, and if all speakers are the same efficiency then all will be 89dB at 9:00 on the volume knob. If a less efficient speaker (80dB for example), less volume.
This relates to watts in the following way:
To calculate power required, you need to know the load. A higher reactance (ohms) will give you a lower power requirement, so an 8ohm load will require half the current and therefore half the power (watts) to run at the same voltage as the 4ohm speaker.
If you have two speaker systems, which are both 89dB at 2.83V, one (the Marties) is a 4ohm speaker and the other an 8ohm speaker, the 4ohm speaker will require approximately twice the power (watts) at that voltage / sound level, but the same volume knob setting.
The amplifier's power rating is the maximum power that it can produce. A higher power amplifier usually has a higher voltage at its maximum setting (which is also a higher volume), and also a higher current (current times voltage equals watts or P=I x E). Thus an amplifier with higher current, higher voltage, or both will be rated at a higher wattage output.
Most amplifier/speaker pairings run out of current before running out of volume-knob rotation. You might hit your maximum clean output at the 12:00 (or less) point and anything above that starts to become clipped or distorted. Just having more volume knob rotation left doesn't necessarily mean that you have more power available if you are already at the current limit of your amplifier.
The Engineer's version is more complicated in all of the other factors involved, this is the simple version which I believe answers your question.
So what this shows you is that voltage is sound level, a direct relationship.
Your volume knob setting is amplification, which is voltage output, So the same amplifier, set at the same volume knob level (lets say for illustration purposes the 9:00 position is 2.83V output which is the abovementioned 89dB) should give you the same amplification and same voltage output regardless of the speaker load, and if all speakers are the same efficiency then all will be 89dB at 9:00 on the volume knob. If a less efficient speaker (80dB for example), less volume.
This relates to watts in the following way:
To calculate power required, you need to know the load. A higher reactance (ohms) will give you a lower power requirement, so an 8ohm load will require half the current and therefore half the power (watts) to run at the same voltage as the 4ohm speaker.
If you have two speaker systems, which are both 89dB at 2.83V, one (the Marties) is a 4ohm speaker and the other an 8ohm speaker, the 4ohm speaker will require approximately twice the power (watts) at that voltage / sound level, but the same volume knob setting.
The amplifier's power rating is the maximum power that it can produce. A higher power amplifier usually has a higher voltage at its maximum setting (which is also a higher volume), and also a higher current (current times voltage equals watts or P=I x E). Thus an amplifier with higher current, higher voltage, or both will be rated at a higher wattage output.
Most amplifier/speaker pairings run out of current before running out of volume-knob rotation. You might hit your maximum clean output at the 12:00 (or less) point and anything above that starts to become clipped or distorted. Just having more volume knob rotation left doesn't necessarily mean that you have more power available if you are already at the current limit of your amplifier.
The Engineer's version is more complicated in all of the other factors involved, this is the simple version which I believe answers your question.
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