The loudness of a jack hammer is 96 dB. Its sound intensity is about [tex]$\sqrt{ } 0.004 v$[/tex]. The loudness of a compactor is 94 dB, its sound intensity is about [tex]$\sqrt{ } 0.0025 v$[/tex]. The sound intensity of the jack hammer is about how many times the sound intensity of the compactor?
Answer (2)
The sound intensity of the jack hammer is 1.6 times the sound intensity of the compactor. This is calculated by dividing the intensity values of both machines. Therefore, the answer is 1.6 .
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Divide the sound intensity of the jack hammer by the sound intensity of the compactor.
Calculate the ratio: 0.0025 0.004 = 1.6 .
The sound intensity of the jack hammer is 1.6 times the sound intensity of the compactor.
The final answer is 1.6 .
Explanation
Understanding the Problem We are given the sound intensity of a jack hammer as 0.004 watts/ m 2 and the sound intensity of a compactor as 0.0025 watts/ m 2 . We need to find how many times greater the sound intensity of the jack hammer is compared to the compactor. This involves finding the ratio of the two sound intensities.
Setting up the Ratio To find the ratio, we divide the sound intensity of the jack hammer by the sound intensity of the compactor: R a t i o = S o u n d I n t e n s i t y o f C o m p a c t or S o u n d I n t e n s i t y o f J a c k H amm er = 0.0025 0.004
Calculating the Ratio Now, we perform the division: R a t i o = 0.0025 0.004 = 1.6
Final Answer The sound intensity of the jack hammer is 1.6 times the sound intensity of the compactor. Therefore, the answer is 1.6 .
Examples
Understanding sound intensity ratios is crucial in various real-world scenarios. For example, in urban planning, knowing how much louder certain construction equipment is compared to others helps in setting noise regulations and implementing noise reduction strategies. Similarly, in workplace safety, assessing the relative loudness of different machines aids in determining the appropriate hearing protection measures for workers. This knowledge also helps in designing quieter equipment and promoting a healthier sound environment.
