Describe each equation below. Identify each term and indicate units. $$\beta = (10 \ dB)log_{10}(\frac{I}{I_0})$$ $$\Delta f = \pm 2f_{emit}(\frac{v_{object}}{v_{wave}})$$
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$I$ is the intensity of the sound wave (W/m^2). $I_0$ is the reference intensity, usually the threshold of human hearing ($10^{-12} \ W/m^2$). Show more…
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In Exercises $85-88,$ use the following information. The relationship between the number of decibels $\beta$ and the intensity of a sound I in watts per square meter is given by $$ \boldsymbol{\beta}=10 \log \left(\frac{I}{10^{-12}}\right) $$ Use the properties of logarithms to write the formula in simpler form, and determine the number of decibels of a sound with an intensity of $10^{-6}$ watt per square meter.
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Recall from Section 4.2 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 $\left(\mathrm{W} / \mathrm{m}^{2}\right)$ 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) $I / I_{0}=1000$
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