Spectrum Level and Overall Level Comparison

This page is designed to demonstrate the relationship between the overall level of a signal and the spectrum level. The overall level reflects the total amound of energy within the signal. For a pure-tone all the energy is at the one frequency - hence a single line on the spectrum at the specified level. For a 'broadband' signal the energy must be added up across the whole of the signal bandwidth. If we assume that the spectrum within that bandwidth is flat, and that the level within each 1Hz is given by the Spectrum Level, then the mathematical relationship is given by:

Overall Level = Spectrum Level + 10 log₁₀(bandwidth)

In the display below you can adjust the overall level wich sets the level of the pure-tone, but also adjusts the spectrum-level of the noise band to have the same overall level. You can also select the tone (and the centre of the band), and also the bandwdith (1/3, 1 or 2 octaves wide). Suggested excercises are given at the bottom of the page.

Overall Level (dB SPL): 65 dB SPL

Center Frequency (Hz): 2000 Hz

Bandwidth: 1 Octave

Spectrum Level = Overall Level - 10 log₁₀(bandwidth)

Suggested Exercises

With the overall level set to 65 dB SPL and the bandwidth set to 1-octave, how much change is there in the spectrum level as you increase the frequency by one octave (e.g. 1kHz to 2kHz) - why does it change in this manner? [hint: doubling the frequency gives doubles the bandwidth]
With the overall level at 65 dB SPL and the frequency set to 2000Hz, how does the spectrum level change as the bandwidth is changed from 1-octave to 2-octaves?
Set the frequency to 250Hz and the overall level to 65 dB SPL and the bandwidth to 1-octave, note the spectrum level. Now increase the frequency by an octave to 500Hz, the spectrum level will decrease, so if we want to restore the spectrum level to what it was we have to increase the overall level. Approximately how much do we need to increase it by?