If one signal is twice the amplitude of another signal, it is + 6 dB relative to it because log 10 2 = 0.3010. When considering amplitudes A of two identical waveforms, the ratio is R = 10 log 10 P 2/ P 1, where P 2and P 1are the amount of power in the two signals. The ratio R of two signals in decibels is: The decibel is 0.10 bel, an obsolete term. This convention works well because it is how we perceive sound and light. Otherwise, the oscilloscope screen might have to be 30 ft tall.ĭecibels are used to compare two quantities in acoustics and elsewhere. The advantage is that it permits the user to see high-amplitude spikes juxtaposed with the low-amplitude noise floor, both in the same display. The scale is logarithmic rather than linear. This power, moreover, is denoted in decibels relative to the Y-axis. In the frequency domain, when you press Math>FFT or send a signal into the RF input, amplitude along the Y-axis displays as power rather than as volts as in the time domain. In the time domain, amplitude is usually shown as volts on a linear scale. RMS is defined in mathematics as the square-root of the mean square. RMS values for non-sinusoidal waveforms are different. The reason we are interested in the RMS value of alternating current that conforms to a sine wave is that it is equal to the amount of direct current that would dissipate the same amount of power in a resistive load. That stands for root-mean-square, and it is used in a variety of disciplines including statistics, water flow, weather forecasting, etc. In an oscilloscope display, for example, we may see branch circuit voltage as 325 V peak-to-peak, but the meaningful figure is 115 to 120 V, depending on your distance from the transformer, wire size and loading. This is new to me, so take that into consideration.In the time domain, amplitude, the dependent variable, is shown in volts relative to the Y-axis. This says that the sound of the siren has an intensity level that is 100 million times the intensity level of a whisper, given they are both the same distance from the listener.įor each 10 db increase, the intensity level is increased by a factor of 10.ġ0 db increase = 10 * the intensity level.Ģ0 db increase = 10^2 * the intensity level.ģ0 db increase = 10^3 * the intensity level.Ĩ0 db increase = 10^8 * the intensity level. Since the siren is 100 db and the whisper is 20 db, then the siren is 80 db higher than the whisper.ĭivide both sides of this equation by 10 to get:

This is presumed to also be at a distance of 30 meters from the source of the whisper. You are given that the decibel level of a whisper is 20 db. The intensity level of the siren is 10 billion times the intensity level of the reference level. This means that the intensity level of the siren is 10^10 times more than the intensity level of the reference level. The intensity level of the signal has increased by a factor of 10^10. The decibel level has increased by 100, since the decibel level of the reference signal is 0. The 1 and the w/900 cancel out and the equation becomes:

If the intensity level of the siren is equal to 1 * 10^-2 * w/m^2. When m = 30, the intensity level of the reference becomes: The intensity level of the reference becomes:

Io is the intensity level of the reference. You can put this solution on YOUR website!

Decibel logarithmic scale