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This may be a bit of a silly question, but it came up during playing and left me wondering. The spell description states that your voice booms "three times as loud as normal", but it leaves open how the volume of a voice is measured.

Two common ways to measure the volume of sound is to measure the pressure difference the sound causes as it travels through air and optionally to transform this level on a logarithmic scale (the Decibel scale). This table lists several things to reference. For example the upper end of a normal conversation sits at 0.02Pa or 60Db.

Now if we mean "three times as loud" on the linear pressure scale, that elevates a normal talking voice to the volume of a TV set. Not very impressive. If we mean "three times as loud" on the logarithmic scale, that comes out above the volume of a stun grenade. Very impressive, though probably a bit unbalanced for a cantrip.

Obviously neither of these interpretations is what the spell creator had in mind. But, then what is?

Etienne Ott
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    I'm not sure your comparison with "normal conversation" holds, when my player used this effect, his base voice volume was "shouting", not "normal conversation", which then got further amplified – Pierre Cathé Sep 05 '19 at 15:54
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    We could use other references, but the effect of the mismatch in volume increase occurs there too. For example the "loudest human voice" is listed at 110Pa and a popped balloon at 283Pa. Does a balloon popping really sound "almost three times as loud" as a human yelling at the top of their lungs? I don't know. – Etienne Ott Sep 05 '19 at 15:58
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    @EtienneOtt well, when you're talking about perceptual loudness, stuff gets complicated. Perceived loudness as reported by humans depends a lot on the duration and frequency of the noise as well as the actual SPL. If you were to somehow constantly consecutively pop balloons next to someone, I imagine that would probably be perceived as extremely loud. – Carcer Sep 05 '19 at 16:09
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    This is really a physics question based on some confusion about how sound pressure scales work. – Mark Wells Sep 05 '19 at 16:25
  • related: https://rpg.stackexchange.com/q/74380/23970 – nitsua60 Sep 06 '19 at 00:36
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    When I read this spell the first time I immediately thought to myself: +9 Db – Bernat Sep 06 '19 at 12:30

3 Answers3

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Our group has ruled similar spells and effects to mean that the sound could be heard 3x as far away.

e.g. if a Shout can be heard reasonably clearly 100 yards away, then Thaumaturgy would make it clearly audible up to 300 yards.
Anyone "close" (undefined) to the Caster would be wanting to cover their ears, and might have a slight ringing afterwards, but no game-mechanical effect.

Black Spike
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    I like this, because it's consistent with how volumes are described as distance-you-can-hear-it in spells like Thunderwave and Knock. It might not be RAW or simulationist physics, but it seems good enough for most practical questions, since usually what one cares about is whether something heard the sound or not. –  Sep 05 '19 at 20:43
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    We have used such effects to be heard in mass-combat, or loud, crowded areas. "I shout to my friend" ... "Sorry, area is too loud" ... "Thaumaturgy! Loud (3x) Voice!" ... "Ok, that should do it" – Black Spike Sep 05 '19 at 20:59
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Ask your DM

This is one of those "get creative" spells like Prestidigitation that is (I think) deliberately left fairly vague because it is meant to be an adaptable utility cantrip geared towards the narrative/problem solving aspect of the game.

A voice can be a whisper, a conversational tone, or a full throated yell. Nevermind how to the amplification is calculated, even the starting sound is subject to a lot of variability. The point is that the voice is amplified.

A player attempting to use Thaumaturgy should inform the DM what sort of effect/benefit they are aiming to achieve and work with the DM to figure out if/how that is achievable.

As Black Spike points out in their good answer, one very easy solution to implement would be to simplify the question to how far the voice carries (since this is probably the more relevant question). If it's three times louder, it can be heard at three times the distance it normally could be heard.

While the Sourcebooks don't seem to quantify this distance in any way, the (an) official DM screen does include this info about audibility:

Audible Distance

Trying to be quiet 2d6 x 5 feet

Normal noise level 2d6 x 10 feet

Very loud 2d6 x 50 feet

Community
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Rykara
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It would be three times the volume on the linear scale. Even when things are measured on a logarithmic scale, we don't use "x times larger" to represent the values on the logarithmic scale itself. For example, an M8.0 earthquake is not twice as powerful as an M4.0 earthquake, but rather 10000x more powerful.

Cacse
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  • I don't think we use "twice as loud" to describe any sounds honestly. We just say "much louder". It's almost exclusively used with reference to size and distance – Exempt-Medic Sep 05 '19 at 16:54
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    This is correct. I work professionally in acoustics and RF electronics, both of which use dB or log scales. One simply never "doubles" an intensity (power, loudness, voltage) by doubling the dB or log scale. Rather, one doubles power by adding 3 dB, voltage by adding 6 dB, etc. One halves those quantities by subtracting those values. – Novak Sep 05 '19 at 21:39
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    Further, physical values are normalized to reference, which is then reported as "0 dB relative to..." whatever. This is explicitly true of acoustic measurements. The upshot of this is that these dB values can be negative, which means doubling those values makes them more negative which is actually smaller. It is physically non-sensical. Casce, feel free to edit this into your answer if you think it improves it. – Novak Sep 05 '19 at 21:41
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    @Novak Not only is it weird for negative values, but it's nonsense because it changes the dimensionality of the quantity. Like, 10 dBm is an amount of power, but 10 dBm times 3 is not. – Mark Wells Sep 06 '19 at 14:13