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Does adding two sounds really increase the sound level by 3 decibels?

Updated: Mar 10, 2023

It is not easy to demonstrate in class that the addition of two sound sources of the same intensity leads to an increase in the sound level of three decibels, a result mentioned in all school books. Indeed, to be able to demonstrate this effect without interference phenomena, it is necessary to use independent sound sources, such as for example white noise.

In this post, we use the FizziQ application to experimentally approach this effect in a very simple way, and to question the students about the interference phenomena for pure tones.

Let's use the FizziQ app on three smartphones. The first will measure the sound level (Measurements tab), and the other two will each emit a "White Noise" that can be found in the application's sound library (Tools tab -> Sound library).

The sound level of white noise is variable over very short periods and therefore the sound level measurement must be averaged to obtain a stable measurement. For this we use an option of FizziQ which is filtering, which we find in the Parameter menu of the Tools tab (from version 3.4.9). This filtering, the intensity of which can be adjusted, makes it possible to apply an exponential average to the data.

We adjust the volume of the two transmitting smartphones so that the two sounds are of equivalent sound levels. Then we measure the sound emitted by the two smartphones simultaneously and we then observe an increase in the overall sound level of 3 decibels.

If we have a large class, we can try to add the white noise of 10 student laptops for an increase in sound level of 10 decibels, and open the discussion on logarithms.

We can also use the "Passing Street" sound of the library which is close to white noise and which puts the students in more real situations. We can then approach the concept of noise.

Now let's try to use a pure signal instead of white noise. For example, let's use two sounds with a frequency of 600 Hz thanks to the application's frequency synthesizer (Tools tab -> Frequency synthesizer). We note that the result is highly random: indeed, by repeating the experiment several times, we realize that the sound volume can increase by several decibels, but also decrease!

The reason is that two pure tones of the same frequency are not independent. The result of adding the sounds depends on the phase shift between the two sources. If we add two pure tones of the same frequency and in phase, the resultant will have a double amplitude and the sound level will increase by 6 decibels, not 3. On the other hand, two pure tones of the same frequency but out of phase by half a period will have a resulting sound. of zero amplitude. It is on this principle that noise reduction headphones work.

You can also reproduce this effect on a single laptop by using two channels on the synthesizer, and gradually overtaking them.

Finally, if we use two pure tones of different but close frequencies, we then obtain regular interference between the two sounds which creates the beating phenomenon that we described in another video.

The experience of adding sounds is very interesting to perform in class and opens up many educational avenues. With the FizziQ application it is very easy to use.

Happy experimenting!

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