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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.

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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.

This problem has been solved

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