What is RMS?

RMS stands for Reverse Mean Square which is a mathematical equation internally calculated by the RMS-capable tools to calculate measurements in a variety of systems. So, what really happens inside the real world then? What is true RMS? And is there any way to truly measure true RMS value? The only sure way to measure true RMS value is with an instrument that measures RMS directly, but unfortunately, these instruments are few and far between.

In a nutshell, the RMS formula is a mathematical tool used in measuring acoustical wave forms. It calculates the “loudness” of the waves by measuring their frequency response as represented by a sound wave. A particular characteristic of these sounds is their frequency response or how fast they repeat. These waves can also have high levels of turbulent noises called “cavitations” which can make them seem much louder than their actual RMS level. This is why they are often quoted as being able to measure true RMS levels. What is true RMS measurement then?

What is RMS?
What is RMS?

True RMS measurement is achieved when a profiled filter on a microphone can hear the “loudness” of the different noise sources within an ac waveform. For example, let’s say you wanted to hear the sound of water splashing across a pool. If you could hear this noise at several different locations in the pool and time this noise to hear it as it occurs over a period of time, you would be able to determine how many times the water in the pool splashed into the air, and thus calculate the true value. What is true RMS measurement then?

This is actually a fairly simple formula that involves the average power that the water dissipates in a particular time interval. First we need to define our Means, which is simply the amount of power that the water dissipates in one cycle. Then we need to define our Maximum values, which are essentially the maximum amount of power that the water dissipates during one cycle. To do this, we use a function called exponents, which takes an arbitrary range for our Maximum values. The formula then is:

What is RMS then? RMS stands for “resolution mean signal strength.” Using the above formula, we can determine the exact frequency response of any given time period. In audio signal processing, the term “resolution mean wave form” is used to describe the way that the waveform looks when it is plotted against time. What is RMS then?

What is RMS then, but not necessarily what is RMS? If we plot a time vs. frequency plot using the above equation, what we get is called a “periodogram,” which depicts the exact frequency response as it changes through time. The periodogram, or its shape, can be graphed as a curve with a positive slope and a negative slope. (In actual terms, the slope of the curve represents the phase transition that the audio signal undergoes.) If we plot the graph as a square wave, we get what is called a “sonic curve,” which literally means “sonic mean value” in the audio-signal processing terminology.

To calculate RMS, we must be able to determine the root mean square of the phase transition that our audio wave underwent. There are many different methods to determine the root mean square of a phase transition, and they all have different requirements. The only thing that remains common in all of the methods for calculating RMS is the method that we use to determine the RMS value of our audio signal.

The basic equation used to determine RMS (or, the RMS value of an audio signal) is the product of the time period t plus the instantaneous power on the AC source of a sinusoid array, times the difference in frequencies that result from the two sinusoids together, the frequency difference being the sinusoidal bandwidth of their section. In other words, the formula is: at times sinusoidal bandwidth | rms | sine wave | equation | audio} A calculator is useful in helping us solve more complex equations such as the one stated above. Any audio-based calculator will allow us to plug in a sinus-frequencies (t, sine-wave frequency) and our desired waveform, and find the RMS value of the sinus-wave. For those not familiar with RMS, there are some free online calculators (both for Windows and Apple IOS devices) that may help. For those comfortable with Excel and Microsoft Office programs, there are some excellent software packages that will calculate RMS easily and quickly.

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