In dB has always been the formula. In percentages I don't know how it will turn out. As a mathematician, I think its a step in the right direction to question this equation and formulas in determining sounds/noise. I am keenly following your interesting study. Best regards

Signal to noise ratio (SNR) is usually expressed in dB, especially in audio and sound applications, because of the very large dynamic range of human hearing.

As a mathematician, you should ask yourself: If I have a physical quantity x with huge dynamic range, and then, in order to compress its dynamic range, I take the logarithm of x using y = log(x), what are the physical dimensions that I should ascribe to y? If x is power in Watts, for instance, then what units should you give to y = log(x)?

Take some time to answer that now....Look up some series expansions for log(x) for starters..

...What you should conclude is that it is WRONG to construct a new variable y=log(x) whenever x is NOT dimensionless. (The same is true, incidentally, for sin(x), exp(x), etc...)

Rather, what you should do is first make a new dimensionless quantity x'=x/x_ref, where x_ref is any reference value for x. In audio, x_ref is the minimum perceptible sound level. It is set by convention. Then both x' and y=log(x') are dimensionless quantities, and we have mapped dimensionless x' (a ratio) to dimensionless y.

This is roughly what dB is doing, when we take y = 10 log10(x/x_ref) to convert x into dB. We are simply converting one dimensionless ratio into another, but we always remind ourselves and the world that we have made this conversion by including the dimension units dB when reporting y.

For signal to noise ratio (SNR), we have a mean signal power x in Watts, and mean noise power n in Watts. And then:

In your case, if the signal of interest X_SPL has a sound pressure level (SPL) of 50 dB (your teacher, as measured by your sound level meter), and the background noise level N_SPL is 30 dB (as measured by your sound level meter), then the SNR in dB is SNR = 50 dB - 30 dB = 20 dB -- much as you have it at the end of your question.

Thanks for the responses. This cleared up the issue!

When you are dealing with huge ratios (and SNR can be a huge ratio), you need a non-linear scale (in this case log scale) to get "normal" ratios.

And I also agree, Ronald gave you a very good answer.

SNR in dB is a logarithmic power ratio. Logarithms are convenient to work with because multiplications and divisions become additions and subtractions. Also, they provide suitable representations in place of very large ratios.

dB just comes handy, "shrinking" ratios in the orders of magnitude to usually 1- or 2-digit decimal numbers. While the underlying math remains the same, these numbers are easier to perceive than counting the zeroes.

Any % number would simply shift the position of the decimal point, altering nothing substantial on the "zero-counting".

1. The sound perception has a logarithmic characteristic. By increasing the power from 1W to 10W you don't feel that the sound intensity has increased ten times, for that reason the volume potentiometer has exponential characteristic (improperly called logarithmic).

https://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law

2. It is easier to compute the loss/gain in dB metrics. For an amplifiers chain, the total gain is the total sum (not product) of the gain (in dB) of each block.

3. For isotropic radio propagation (Friis formula) the path loss is : L (dB) = 22 + 20log(d/λ), so is easy to compute the loss in in multiples of wavelength, ant total loss by summing up all the losses/gains. From the above formula, each doubling of the distance leads to 6dB power loss.

The dB is a practical scale to represent very large ranges of ratios through logarithmic compression. It also converts the multiplication and division of ratios to an addition and subtraction process.

Best wishes

Sometimes, in the VU scale of audio equipments you find also the % scale under the dB scale. Conventionally, 0 dB corresponds to 100% (reference level). So, you find -3 dB = 75%, -6 dB = 50% and so on. Expressing S/N ratio in dB is more practical than doing it in % values, because signal is normally far higher than noise (in audio hifi gears, tipically 90 - 100 dB), so a % value would be a number with a lot of zeroes, hardly readable.

it is a logarithmic scale its using is more easier than other scales.