Chapter 2: Q22E (page 539)

The Sacramento City Council adopted a law to reduce the allowed sound intensity level of the much-despised leaf blowers from their current level of about 95 dB to 70 db. With the new law, what is the ratio of the new allowed intensity to the previously allowed intensity?

Short Answer

Expert verified

The ratio of the new allowed intensity to the previously allowed intensity is $3.2 \times 10^{- 3}$

Step by step solution

STEP 1 Concept of the difference between the sound intensity levels for two different intensities

The formula is given as $β_{2} - β_{1} = 10 \log (\frac{l_{2}}{l_{1}})$ where, $l_{2}$ is the new intensity and $l_{1}$ is the previous intensity

Calculate the ratio of the new allowed intensity to the previously allowed intensity

New allowed intensity is $l_{2}$ and the previously allowed intensity is $l_{1}$ , to find the ratio of these two use the equation $β_{2} - β_{1} = 10 \log (\frac{l_{2}}{l_{1}})$ and substitute the values in the equation we get,

$(70 db - 95 db) = 10 \log (\frac{l_{2}}{l_{1}}) - 25 db = 10 \log (\frac{l_{2}}{l_{1}}) - 2.5 = 10 \log (\frac{l_{2}}{l_{1}})$

Note that $10^{\log (x)} = x$

Therefore,

$10^{- 2.5} = (\frac{l_{2}}{l_{1}}) (\frac{l_{2}}{l_{1}}) = 3.2 \times 10^{- 3}$

Thus, the ratio of the new allowed intensity to the previously allowed intensity is $3.2 \times 10^{- 3}$

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The Sacramento City Council adopted a law to reduce the allowed sound intensity level of the much-despised leaf blowers from their current level of about 95 dB to 70 db. With the new law, what is the ratio of the new allowed intensity to the previously allowed intensity?

Short Answer

Step by step solution

STEP 1 Concept of the difference between the sound intensity levels for two different intensities

Calculate the ratio of the new allowed intensity to the previously allowed intensity

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