# What amplitude ratio to achieve "sound pressure level" ratio?

I would like to create a sound with three sine waves. The first sine wave is the fundamental frequency (f0), the second wave is a harmonic (f2), the third is also a harmonic (f4) of the base frequency. The harmonics should have a sound pressure level ratio (between the sound pressure level of the fundamental and the sound pressure level of the harmonics) to the base freqency of +/- 15dB.

What factor do I need to multiply the amplitude of the sine waves with, to achieve the +/- 15dB sound pressure level ratio?

I generate the sound inside a program and I can control the amplitude of the sine waves.

I have tried

1. this table that led me to the conclusion: a2 = a0 / 10 / 3.162 (which resembles `-15dB = 10 * log(a0/a2) `
2. this formula: `-15dB = 20 * log(a0/a2)` that led me to the conclusion a2 = a0 * 0.1778

Those two give significantly different results. Which one should I use to calculate the amplitude to achieve the sound pressure level ratio?

``````f0 = f2 / 2 = f4 / 4
a2 = ? * a0
a4 = ? * a0
``````
• Ok so the first issue with this is that Sound Pressure Level and Sound Intensity (acoustic intensity) are not the same thing. The "table" you refer to is from a hearing loss site dealing with "sound intensity". You need to check your algorithm based on the Sound Pressure Level formula.
– Mark
Mar 17, 2021 at 13:17
• @Mark , I infer that you refer to the second formula: -15dB = 20 * log(a0/a2) for the SPL. is that correct? Mar 18, 2021 at 12:05
• that looks more like it.
– Mark
Mar 18, 2021 at 12:24