How to measure loudness
Sound pressure level (SPL)
is used to measure loudness in this case.
The unit of measurement is dB(SPL).
- Sound pressure meter is an instrument used to measure dB(SPL). Cheap sound pressure meters can be bought starting at 20 USD.
- The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity. The physical quantity is sound pressure measured in Pascals(Pa). Sound pressure level is defined as
Lp = 20 log10 p1/p0
where p0
is the reference value.
- The reference value used is threshold of human hearing (sound pressure of air).
- It's important to note that there's much more to subjective perception of loudness than sound pressure alone.
Reference values for loudness
Sound source Sound Pressure Level dB(SPL)
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Hearing threshold 0
Rustling leaves, light breathing 10
Calm room, bedroom at night 20-30
Quiet library 40
Normal conversation at 1m 50-70 (avg 60)
TV (at home level) at 1m 60
Vacuum cleaner at 1m 70
Busy street at 5m 80
Heavy traffic, diesel truck at 10m 90
Jackhammer at 1m 100
Chainsaw at 1m 110
Threshold of discomfort 120
Threshold of pain 130
From thereon to clear any confusion I propose that apartment friendly volume would be in 50-60 dB range. And 70 dB an upper bound for not pissing anyone off. 40 dB being whisper quiet.
Loudness of cranked tube amplifier
- To calculate the sound pressure level of an amplifier you have to know the
Speaker Sensitivity
. Speaker sensitivity is expressed in dB(SPL) per 1 Watt measured at a 1m distance.
- The off-the-shelve speaker cabinets usually don't have this value on the spec-sheet. Generally this value is in the 87-92 dB range. For professional grade, highly efficient cabinets speaker sensitivity is in 100-110 dB range.
- Assuming the speaker sensitivity of 90 dB and a single 1x12, a cranked 1 Watt amplifier will be 90 dB at 1m distance. Cranked 1W amplifier is VERY LOUD.
Amplifier power Sound Pressure Level dB(SPL)
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1 W 90 dB
5 W 97 dB
10 W 100 dB
22 W 103 dB
50 W 107 dB
100 W 110 dB
120 W 110.8 dB
In other words, 10W amplifier will be twice as loud as 1W amp, and a 100W four times as loud as 1W amp.
Attenuating to apartment volume
To bring a cranked 1W amp to 60 dB we have to lose roughly -30 dB. That would be 1/8 of the volume. The power of the amplifier have to be attenuated down to 0.001 W. That's 0.1% of power output.
In other words, to power a speaker at 60 dB sound pressure level we need 0.001W of power.
Amplifier power Sound Pressure Level dB(SPL)
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0.001 W 60 dB
0.01 W 70 dB
0.1 W 80 dB
For a 22W amplifier we have to lose roughly -40 dB, 1/16 of the volume, 0.01% of power output.
Conclusions
The attenuator suggested by Bartek (Weber Mini Mass) should do the job as it can attenuate down to -50 dB.