# Noise perception by humans - one vs two of the same noisy appliance - will the noise be "double"?

If I have a clothes washer in a room versus two of the same machine making the same noise, will the noise level be perceived by humans as twice the level it was before?

I'm pretty sure sound is in a logarithmic scale, so adding two logs would lead me to believe "no", but we're talking about humans here.

• We choose to quantify sound on a logarithmic scale exactly because that lines up roughly with how humans perceive loudness. Nov 20, 2019 at 2:58
• So if the clothes washer is 50 dB noisy, two of the same machine would be 53 dB, which means it would be "barely" louder to a human? Nov 20, 2019 at 3:01
• Definitely noticeably louder (i.e. people can tell it went from one washer to two) but not a whole new level of loudness. Nov 20, 2019 at 3:29
• @slantalpha a 3 dB difference is double, not barely different
– Mick
Nov 20, 2019 at 7:19

## 3 Answers

Well, if you want to be mathematically correct (in an objective manner), the noise will be doubled. As niels nielsen mentioned doubling the power will yield a 3 dB increase. Now, whether this results in a doubling of loudness as a perception metric, then the answer is most probably no.

According to the book Communication Acoustics by Pulkki and Karjalainen and further references therein, as well as the very well known Equal Loudness contours (Wikipedia link) (also known as Fletcher & Munson curves), you can see that the perception of loudness is definitely frequency dependent. Not only that, but the dependence is also amplitude (or level) dependent!

In addition to that, the aforementioned curves are extracted from experiments made with pure tones. Due to some psychoacoustic phenomena such as the increase of perceived loudness when the spectrum covers more than one critical bandwidth (for more info refer to Communication Acoustics by Pulkki and Karjalainen or a book called Psychoacoustics - Facts and Models by Fastl and Zwicker, page 202) the loudness is also bandwidth dependent in a non-linear way.

It has been proposed in Psychoacoustics - Facts and Models book that, as a rule of thumb, a 10 dB increase in level (but this is for pressure not power) results in a doubling of loudness for a 1 KHz plane wave tone. As you can imagine by now, this is (as mentioned) a rule of thumb, since the phenomenon of subjective loudness perception is far more complex than this linear level-loudness proposal.

Finally, I apologize for not being able to provide more than just links to pages showing the book (and not the books themselves) and I hope I didn't complicate things too much.

• It does not matter whether level difference is calculated from pressure of of power: in the first case it is 20 times the log of the pressure ratio, in the second case 10 times the log of the power ratio.
– user137289
Nov 29, 2019 at 13:47
• Yes, that's true. I just wanted to make clear that the proposal was based on sound pressure. Maybe I didn't state it very well. Thanks for the comment. Nov 29, 2019 at 14:01

Your ears detect loudness on a logarithmic scale, where doubling the strength of the noise source results in a slight but noticeable increase in the perceived loudness, which is +3dB when measured on a sound level meter.

So, if one washing machine generates (for example) a 75dB noise level, adding a second washing machine will measure (75 + 3) or 78dB on a sound level meter.

According to this article, the loudness discrimination threshold for human hearing is around 0.6 db. I've seen other articles that place it at around 1.6 db. It seems to be dependent on the frequency spectrum of the sound.

• Depends on the frequency spectrum, yes, but also whether the change occurs while you are listening, or if it occurs with a break in-between (i.e., you came back the next day... could you tell a difference?) Nov 23, 2019 at 0:35
• Both points are certainly true! Nov 23, 2019 at 0:45