Watts vs. dB output on volume knob

[BMead]

I recently purchased a Yamaha RX-V861 with a maximum output wattage of 105W per channel. The volume knob and associated display go from -80dB to 16.5dB.

How do I judge the total dB output of the speakers I’m listening to?

If I understand what I’ve read the dB output vs. wattage output doesn’t make sense. I’ve read that every time you double the output wattage you add 3dB of volume. Similarly every time you increase the output wattage by 10 times you increase the dB output by 10dB. (both are comparable watts to dB). Let’s use the 10dB per 10 x output wattage.

If I assume a 0 dB volume level means 1 watt (with a true output in dB equal to that of the speaker sensitivity) the numbers don’t work out.

1W*10 = 10 watts with an increase of 10dB
10W*10 = 100 watts with a total increase of 20dB
Already I’m above the 16.5dB of the volume knob with 5 watts to spare (negligible)

Is the 10*output wattage giving 10dB too much of a generalization?


A second question, ignoring the receivers display:

If I have two Klipsch RF-5 speakers with a sensitivity of 99dB @ 1 meter is the following calculation correct?

99dB @ 1 watt @ 1 meter
109dB @ 10 watts @ 1 meter
119dB @ 100 watts @ 1 meter

6dB of loss every time you double your distance to the speakers
1m = 0dB loss
2m = 6dB loss
3m = 12dB loss

Two speakers gives a gain of 3dB

Putting the speakers in a room (non anechoic) usually gives you a 4dB increase in level.

To sum it up if I’m sitting 3 meters from my pair of Klipsch RF-5 speakers with my volume at max (approximately 100W) I should have a volume level of 99+20-12+3+4 = 114dB correct? Obviously there will be a fudge factor in there but is that close?

If I add in two surrounds (rs-3) and a center speaker (rc-3) does that add 3dB per speaker?

I’m mostly curious about this for general understanding as well as protecting my hearing. I believe I’ve read that 115dB for any amount of time over a few seconds will cause permanent damage to the ear drum. Thank you in advance for your responses!

 

[mtrycrafts]

I recently purchased a Yamaha RX-V861 with a maximum output wattage of 105W per channel. The volume knob and associated display go from -80dB to 16.5dB.

How do I judge the total dB output of the speakers I’m listening to?

If I understand what I’ve read the dB output vs. wattage output doesn’t make sense. I’ve read that every time you double the output wattage you add 3dB of volume. Similarly every time you increase the output wattage by 10 times you increase the dB output by 10dB. (both are comparable watts to dB). Let’s use the 10dB per 10 x output wattage.

If I assume a 0 dB volume level means 1 watt (with a true output in dB equal to that of the speaker sensitivity) the numbers don’t work out.

1W*10 = 10 watts with an increase of 10dB
10W*10 = 100 watts with a total increase of 20dB
Already I’m above the 16.5dB of the volume knob with 5 watts to spare (negligible)

You forgot about the input signal level with this example.

You increase the input signal level, you increase the output power with the volume at 0dB. If you use a signal level of -30dBFS, as an example since that is what is on some, not all, test DVDs, then you would be hearing and measuring around 75dB spl. You input a signal level to -20dB FS, a 10 dB change, you would be getting 85 dB spl.

A second question, ignoring the receivers display:

If I have two Klipsch RF-5 speakers with a sensitivity of 99dB @ 1 meter is the following calculation correct?

99dB @ 1 watt @ 1 meter
109dB @ 10 watts @ 1 meter
119dB @ 100 watts @ 1 meter

Yes, that is correct and the above applies, input signal level.

6dB of loss every time you double your distance to the speakers
1m = 0dB loss
2m = 6dB loss
3m = 12dB loss
Putting the speakers in a room (non anechoic) usually gives you a 4dB increase in level.

That applies in free, open space, very large auditoriums, not in normal listening rooms at home. Wall reinforcement will not give that 6 dB of loss, perhaps 4-5dB, maybe.


Two speakers, same identical signal(mono) gives a gain of 3dB if not both amplified. If both are amplified, you double the power and area of of speaker surface, so it is about 6dB unless you have an interaction between the two and some cancellations.

To sum it up if I’m sitting 3 meters from my pair of Klipsch RF-5 speakers with my volume at max (approximately 100W) I should have a volume level of 99+20-12+3+4 = 114dB correct? Obviously there will be a fudge factor in there but is that close?

Well, you will lose about -8 dB spl and since you are not operating mono in speakers, you won't be getting that +3 and +4. If your signal is full scale, at 0 on the master volume, that is about what you should get, IF the speaker is capable of that spl level without reaching compression and can stand the distortion with many speakers.

If I add in two surrounds (rs-3) and a center speaker (rc-3) does that add 3dB per speaker?

No, you ar enot sending mono in phase at the same instant to all. And, being in their respective locations, I doubt they would add like that.

I’m mostly curious about this for general understanding as well as protecting my hearing. I believe I’ve read that 115dB for any amount of time over a few seconds will cause permanent damage to the ear drum. Thank you in advance for your responses!

Yes, you don't want to damage your hearing.

 

[OttoMatic]

How do I judge the total dB output of the speakers I’m listening to?

Well, I see you've done quite a few calculations below, but I would use an SPL meter. You could use this to gauge when you reach you specified output rating of the speaker, at 1 meter, using whatever signal is specified (white noise, pink noise, 1kHz test tone, etc). It would be best to do this outside or in some location where you're not going to get a lot of room reinforcement. If you wanted to, it's possible.

But yeah, I'd measure your actual sound levels with an SPL meter.

If I understand what I’ve read the dB output vs. wattage output doesn’t make sense. I’ve read that every time you double the output wattage you add 3dB of volume. Similarly every time you increase the output wattage by 10 times you increase the dB output by 10dB. (both are comparable watts to dB). Let’s use the 10dB per 10 x output wattage.

That's a very good generalization. Here's the equation:

10*log( W2/( W2 - W1) ) = P

where W2 is the "second" wattage and W1 is the "first, and P is power in dB.

So, if you doubled your power from 5W (this will be P1) to 10W (this P2), you get

10*log ( 10 / ( 10-5 ) )
= 10*log ( 2 ) ----- note here that the stuff in the parens just becomes the ratio of the increase in power, in this case it's doubled.

= 10*3.01029 ~= 3 db

which is your 3 dB increase for a doubling of power.

Similarly, for a 10x increase in power, you'd get:

10*log(10) = 10 dB

If I assume a 0 dB volume level means 1 watt (with a true output in dB equal to that of the speaker sensitivity) the numbers don’t work out.

0 dB on the knob doesn't really mean 1 W at the output. I usually tend to think that it means there is neither amplification nor attenuation applied at the preamp stage. I've measured a few preamps from input to output, and at 0 dB, I get pretty close to a pass-through signal. Now, since that 0 dB number is applied to the preamp stage, the power output at the speaker terminals will be dependent on the amplifier attached, so it could be anything.

If you were actually to do the (rather non-scientific) test I suggested initially, you'd find that a 1W output at the amplifier will actually correspond to a much lower number on the volume knob display. I don't know what it'll be, but it'll be less than 0 dB on the display.

Is the 10*output wattage giving 10dB too much of a generalization?

Nope, it's exactly correct.

 

[BMead]

Thanks

Kudos for the responses! As an Electrical Engineer I love all the math. Thanks again for the in depth responses!