- #1

ngn

- 20

- 1

- TL;DR Summary
- If time-averaged power of a sinusoidal wave is proportional to the square of the amplitude of the wave and the square of the angular frequency of the wave, then why do decibels measurements only require an amplitude?

Hello,

It has been difficult to find a clear answer to this question. I've found some sources stating that the power of a sound wave depends upon both amplitude and frequency. I've found other sources stating that the power of a sound only depends on amplitude. I've found sources stating that power only depends on amplitude (and not frequency) for electromagnetic waves, but with mechanical waves (e.g., sound) both amplitude and frequency are important. And, I've found sources stating that amplitude and frequency only affect power with light waves but with sound waves, only amplitude matters.

If both amplitude and frequency are important for calculating the power of a sound wave, why is it that when it comes to calculating decibels, frequency does not matter? For example, if a 500 Hz and a 1000 Hz pure tone both have the same RMS normalized amplitude measurement (e.g., 0.50), then they both have the same decibel measurement (20*log(0.50) = -6 dB FS). Similarly, if a 500 Hz and 1000 Hz tone both have the same sound pressure (e.g., 10 Pa), then they both have the same dB SPL (20*log(10/.000020) = 114 dB SPL). The fact that you calculate decibels on amplitude-based measurements only suggests that frequency is not important in calculating power. Is this correct?

It has been difficult to find a clear answer to this question. I've found some sources stating that the power of a sound wave depends upon both amplitude and frequency. I've found other sources stating that the power of a sound only depends on amplitude. I've found sources stating that power only depends on amplitude (and not frequency) for electromagnetic waves, but with mechanical waves (e.g., sound) both amplitude and frequency are important. And, I've found sources stating that amplitude and frequency only affect power with light waves but with sound waves, only amplitude matters.

If both amplitude and frequency are important for calculating the power of a sound wave, why is it that when it comes to calculating decibels, frequency does not matter? For example, if a 500 Hz and a 1000 Hz pure tone both have the same RMS normalized amplitude measurement (e.g., 0.50), then they both have the same decibel measurement (20*log(0.50) = -6 dB FS). Similarly, if a 500 Hz and 1000 Hz tone both have the same sound pressure (e.g., 10 Pa), then they both have the same dB SPL (20*log(10/.000020) = 114 dB SPL). The fact that you calculate decibels on amplitude-based measurements only suggests that frequency is not important in calculating power. Is this correct?