<p>In general, any added sound increases the total <a href="https://en.wikipedia.org/wiki/Sound_pressure_level" rel="nofollow noreferrer">sound pressure level (SPL)</a>, even if this sound alone has a smaller SPL than that of the background sound of the room. This is right when the added sound is <a href="https://en.wikipedia.org/wiki/Coherence_(physics)" rel="nofollow noreferrer">incoherent</a> with the background sound.</p>
<p>However, the SPLs with and without the added sound could be considered as about equal when the increase of SPL can be too small to be perceived and/or to be measured; have a try with this online calculator <a href="http://www.sengpielaudio.com/calculator-leveladding.htm" rel="nofollow noreferrer">here</a>: if you add two sources of 60 dB SPL and 40 dB SPL, the total  level is 60.043 dB SPL.</p>
<p>The sound envelop can quickly vary with time. As the SPL involves the calculation of an average over a duration (referred as <em>time constant of integration</em> or <em>time-weighting</em> in <a href="https://en.wikipedia.org/wiki/Sound_level_meter" rel="nofollow noreferrer">SPL meters</a>), SPL may increase only at particular moments if this duration is in the range of the speech word duration.</p>
<p>In some particular cases of <a href="https://en.wikipedia.org/wiki/Coherence_(physics)" rel="nofollow noreferrer">coherent</a> sounds (<a href="https://en.wikipedia.org/wiki/Active_noise_control" rel="nofollow noreferrer">active noise control</a> or <a href="https://en.wikipedia.org/wiki/Standing_wave" rel="nofollow noreferrer">standing waves</a>), the total SPL can even be reduced by adding a sound which phase is offset compared to that of the background sound.</p>
<h2>If you are familiar with mathematical notations</h2>
<p>At a given location, the change in SPL <span class="math-container">$\Delta L_{T,\Delta t}(t)$</span> between times <span class="math-container">$t$</span> and <span class="math-container">$t-\Delta t$</span> is proportional to:</p>
<p><span class="math-container">$ \Delta L_{T,\Delta t} (t) \sim  log_{10}( \frac{p_{rms,T}(t)}{p_{rms,T}(t-\Delta t)} )$</span></p>
<p>where <span class="math-container">$ p_{rms,T}(t) = \sqrt{ mean( p^2(t),T)}$</span> is the <a href="https://en.wikipedia.org/wiki/Root-mean-square" rel="nofollow noreferrer">RMS</a> of pressure <span class="math-container">$p(t)$</span> over duration <span class="math-container">$T$</span>.</p>
<p>Then, adding an incoherent sound at <span class="math-container">$t$</span> (or between <span class="math-container">$t-T$</span> and <span class="math-container">$t$</span>) increases the RMS pressure <span class="math-container">$p_{rms,T}(t)$</span> as compared to <span class="math-container">$p_{rms,T}(t - \Delta t)$</span>, so <span class="math-container">$ \Delta L_{T,\Delta t}&gt;0$</span> (i.e. the SPL increases)</p>

CC BY-SA 4.0
2023-10-31T10:18:09.297Z
2023-10-31T18:39:46.980Z
2023-10-31T18:39:46.980Z
Noil
<p>Human hearing sensitivity is approximately logarithmic, leading to the use of <a href="https://www.britannica.com/science/sound-physics/The-decibel-scale" rel="nofollow noreferrer">decibel scale</a> to measure sound level.</p>
<p>Decibels don't add up directly. For unrelated sounds, the formula is (see e.g. <a href="http://www.sengpielaudio.com/calculator-spl.htm" rel="nofollow noreferrer">this source</a> for details):</p>
<p><span class="math-container">$$ SPL(A+B) = 10 \times \log_{10}\left(10^{SPL(A)/10} + 10^{SPL(B)/10}\right)$$</span></p>
<p>Some practical examples on how this works:</p>
<ul>
<li>Normal <strong>60 dB</strong> conversation is going on. Television is turned on at <strong>60 dB</strong> volume level. Total sound level in room increases to <strong>63 dB</strong>.</li>
<li>Vacuum cleaner is making <strong>80 dB</strong> noise. Television is again turned on at <strong>60 dB</strong>. Total sound level increases to <strong>80.04 dB</strong>.</li>
</ul>
<p>As you can see, quieter noises or even noises at the same sound level do not make a huge difference to the total sound level. Due to the logarithmic nature of hearing, loudest sound dominates.</p>
<p>One extra complication is <a href="https://en.wikipedia.org/wiki/Basilar_membrane#Frequency_dispersion" rel="nofollow noreferrer">human's ability to separate sounds by frequency</a>. A high-pitched noise will be noticed even if there is a louder low-frequency sound in the background, and vice-versa, although <a href="https://en.wikipedia.org/wiki/Auditory_masking" rel="nofollow noreferrer">masking</a> may occur.
Due to the human <a href="https://en.wikipedia.org/wiki/Loudness" rel="nofollow noreferrer">non-linear perception of loudness</a> across frequency, <a href="https://en.wikipedia.org/wiki/A-weighting" rel="nofollow noreferrer">A-weighting</a> is used to better assess SPL when human hearing is of relevance.</p>

CC BY-SA 4.0
2023-10-31T19:00:38.300Z
2023-11-20T19:02:52.590Z
2023-11-20T19:02:52.590Z
jpa
<p>Let me add to @Noil's answer a little bit of physical interpretation.</p>
<p>Every additional sound adds sound energy and the total sound energy increases.The resulting RMS sound pressure level is proportional to the square-root of the sound intensity which is nothing else than the sound energy per second arriving to your ears.</p>
<p>In how far humans notice any difference is another question that is also addressed by others.</p>

CC BY-SA 4.0
2023-10-31T18:05:43.840Z
2023-10-31T19:09:06.837Z
2023-10-31T19:09:06.837Z
WMXZ
<p>I am a computer engineer and I am not an expert in physics. I read about <a href="https://svantek.com/academy/sound-pressure-level-spl/" rel="nofollow noreferrer">Sound Pressure Level</a> from different references but I can't solve my problem. My question is: if we turn on the TV, is the sound pressure level of the room increased definitely? In other words, in the room we have different sounds; if the sounds in the room are louder than the sounds created by TV, does the sound pressure level increased or not? why?</p>

<sound-propagation><sound><acoustic>
If we turn on a TV, is the sound pressure level of the room increased definitely?
# If we turn on a TV, is the sound pressure level of the room increased definitely?

(Asked by: username_0 on 2023-10-31)

I am a computer engineer and I am not an expert in physics. I read about [Sound Pressure Level](https://svantek.com/academy/sound-pressure-level-spl/) from different references but I can't solve my problem. My question is: if we turn on the TV, is the sound pressure level of the room increased definitely? In other words, in the room we have different sounds; if the sounds in the room are louder than the sounds created by TV, does the sound pressure level increased or not? why?

**Tags:** sound-propagation, sound, acoustic


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## 3 answers

### Answer by username_1 on 2023-10-31. Score: 4

In general, any added sound increases the total [sound pressure level (SPL)](https://en.wikipedia.org/wiki/Sound_pressure_level), even if this sound alone has a smaller SPL than that of the background sound of the room. This is right when the added sound is [incoherent](https://en.wikipedia.org/wiki/Coherence_(physics)) with the background sound.

However, the SPLs with and without the added sound could be considered as about equal when the increase of SPL can be too small to be perceived and/or to be measured; have a try with this online calculator [here](http://www.sengpielaudio.com/calculator-leveladding.htm): if you add two sources of 60 dB SPL and 40 dB SPL, the total level is 60.043 dB SPL.

The sound envelop can quickly vary with time. As the SPL involves the calculation of an average over a duration (referred as *time constant of integration* or *time-weighting* in [SPL meters](https://en.wikipedia.org/wiki/Sound_level_meter)), SPL may increase only at particular moments if this duration is in the range of the speech word duration.

In some particular cases of [coherent](https://en.wikipedia.org/wiki/Coherence_(physics)) sounds ([active noise control](https://en.wikipedia.org/wiki/Active_noise_control) or [standing waves](https://en.wikipedia.org/wiki/Standing_wave)), the total SPL can even be reduced by adding a sound which phase is offset compared to that of the background sound.

## If you are familiar with mathematical notations

At a given location, the change in SPL $\Delta L\_{T,\Delta t}(t)$ between times $t$ and $t-\Delta t$ is proportional to:

$ \Delta L\_{T,\Delta t} (t) \sim log\_{10}( \frac{p\_{rms,T}(t)}{p\_{rms,T}(t-\Delta t)} )$

where $ p\_{rms,T}(t) = \sqrt{ mean( p^2(t),T)}$ is the [RMS](https://en.wikipedia.org/wiki/Root-mean-square) of pressure $p(t)$ over duration $T$.

Then, adding an incoherent sound at $t$ (or between $t-T$ and $t$) increases the RMS pressure $p\_{rms,T}(t)$ as compared to $p\_{rms,T}(t - \Delta t)$, so $ \Delta L\_{T,\Delta t}>0$ (i.e. the SPL increases)


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### Answer by username_2 on 2023-10-31. Score: 4

Human hearing sensitivity is approximately logarithmic, leading to the use of [decibel scale](https://www.britannica.com/science/sound-physics/The-decibel-scale) to measure sound level.

Decibels don't add up directly. For unrelated sounds, the formula is (see e.g. [this source](http://www.sengpielaudio.com/calculator-spl.htm) for details):

$$ SPL(A+B) = 10 \times \log\_{10}\left(10^{SPL(A)/10} + 10^{SPL(B)/10}\right)$$

Some practical examples on how this works:

* Normal **60 dB** conversation is going on. Television is turned on at **60 dB** volume level. Total sound level in room increases to **63 dB**.
* Vacuum cleaner is making **80 dB** noise. Television is again turned on at **60 dB**. Total sound level increases to **80.04 dB**.

As you can see, quieter noises or even noises at the same sound level do not make a huge difference to the total sound level. Due to the logarithmic nature of hearing, loudest sound dominates.

One extra complication is [human's ability to separate sounds by frequency](https://en.wikipedia.org/wiki/Basilar_membrane#Frequency_dispersion). A high-pitched noise will be noticed even if there is a louder low-frequency sound in the background, and vice-versa, although [masking](https://en.wikipedia.org/wiki/Auditory_masking) may occur.
Due to the human [non-linear perception of loudness](https://en.wikipedia.org/wiki/Loudness) across frequency, [A-weighting](https://en.wikipedia.org/wiki/A-weighting) is used to better assess SPL when human hearing is of relevance.


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### Answer by username_3 on 2023-10-31. Score: 0

Let me add to @username_1's answer a little bit of physical interpretation.

Every additional sound adds sound energy and the total sound energy increases.The resulting RMS sound pressure level is proportional to the square-root of the sound intensity which is nothing else than the sound energy per second arriving to your ears.

In how far humans notice any difference is another question that is also addressed by others.


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