Recall from Section 0.5 that the loudness of a sound indecibels (dB) is given by = 10

Chapter 3, Problem 38

(choose chapter or problem)

Recall from Section 0.5 that the loudness \(\beta\) of a sound in decibels (dB) is given by \(\beta=10 \log \left(I / I_{0}\right)\), where I is the intensity of the sound in watts per square meter \(\left(W / m^{2}\right)\)

 and \(I_{0}\) is a constant that is approximately the intensity of a sound at the threshold of human hearing. Find the rate of change of \(\beta\) with respect to I at the point where

(a) \(I / I_{0}=10\)

(b) \(I / I_{0}=100\)

(c) \(I / I_{0}=1000\).

Equation Transcription:

Text Transcription:

beta

beta=10 log (I/I_0)

(W/m^2)

I_0

I/I_0 = 10

I/I_0 = 100

I/I_0 = 1000