The sound levels of two sources of sound are measured. The sound level of the fi

Question

The sound levels of two sources of sound are measured. The sound level of the first source is 20 dB and the sound level of the second source is 45 dB. Which one of the following statements is correct?

A source with twice the intensity of the second source would have a sound level of 80 dB

The intensity of the second source is 316 times greater than the intensity of the first source.

It is impossible to compare the intensities of the two sources by sound level because sound level is not related to intensity.

The intensity of the second sound is 2.25 times greater than the intensity of the first sound.

The first source is louder than the second source.

Explanation / Answer

dB level = 10 log10 (I / Io)
where I is intensity of sound and Io is the minimum intensity of sound that we can hear.
If there are tow sources of intensities I1 and I2 and sound level of d1 and d2 dB respectively,
d1 = 10 log (I1 / Io) and
d2 = 10 log ( I2 /Io) subtracting the two we get
d2 - d1 = 10log (I2/I1)

For intensity ratio of 2 , difference in dB level is 10 log(2) = 3. Hence first statement is wrong.
For d2 - d1 = 25 , intensitiy ratio is 102.5 = 316.2, hence second statement is correct.

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