Question

The root means square amplitude of a sound reads 1.084 pascals, what is the dB Amplitude of the sound (dB reference for the sound pressure level is 20 micro Pascal)?

Answer 1

To calculate the dB amplitude of a sound given its root mean square (RMS) amplitude, you can use the formula:

dB = 20 * log10(A / Aref)

Where:

• dB is the decibel amplitude
• A is the RMS amplitude of the sound
• Aref is the reference amplitude (in this case, 20 micro Pascal)

Let's substitute the values into the formula:

dB = 20 * log10(1.084 pascals / 20 micro Pascal)

First, let's convert the reference amplitude to pascals:

20 micro Pascal = 20 * 10^(-6) Pascal = 2 * 10^(-5) Pascal

Now we can calculate the dB amplitude:

dB = 20 * log10(1.084 pascals / 2 * 10^(-5) Pascal)

dB = 20 * log10(54.2)

Using a calculator, the logarithm of 54.2 is approximately 1.733

dB = 20 * 1.733

dB ≈ 34.66

Therefore, the dB amplitude of the sound is approximately 34.66 dB.