Suppose the purr of a cat has a sound intensity that is 340 times greater than the threshold level. Find the decibel value for this cat's purr. Round to the nearest decibel.
Question
Suppose the purr of a cat has a sound intensity that is 340 times greater than the threshold level. Find the decibel value for this cat's purr. Round to the nearest decibel.
Solution
To find the decibel value for the cat's purr, we can use the formula for sound intensity level in decibels:
L = 10 * log10(I/I0)
where:
- L is the sound level in decibels,
- I is the intensity of the sound wave, and
- I0 is the reference intensity (the quietest sound that the average human ear can hear), typically 10^-12 watts per square meter.
In this case, the intensity of the cat's purr is 340 times greater than the threshold level, so I = 340 * I0.
Substituting this into the formula gives:
L = 10 * log10(340 * I0 / I0) = 10 * log10(340) = 10 * 2.53 = 25.3 decibels
Rounding to the nearest decibel gives a sound level of 25 decibels for the cat's purr.
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