Your ears are sensitive to differences in pitch, but they are not very sensitive to differences in intensity. You are not capable of detecting a difference in sound intensity level of less than 1 dB. By what factor does the sound intensity increase if the sound intensity level increases from 60 dB to 61 dB

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Oseni Oseni · Answer 1 · 2020-03-31T03:22:08+02:00

Answer:

1.29

Explanation:

The level of intensity of sound (β) (in decibels, dB) is given by:

β = [tex]10log_{10}(\frac{I}{I_0} )[/tex], where I = sound intensity in watts per meter squared and [tex]I_0[/tex] = reference intensity.

Change in sound intensity level (Δβ) = [tex]\beta _2 - \beta _1[/tex] = 61 - 60 = 1

Δβ = [tex]10log_{10}(\frac{I_2}{I_0}) - 10log_{10}(\frac{I_1}{I_0})[/tex] = 1

[tex]10log_{10}(\frac{I_2}{I_0})/(\frac{I_1}{I_0})[/tex] = 1

[tex]10log_{10}(\frac{I_2}{I_1})[/tex] = 1

[tex]\frac{I_2}{I_1}[/tex] = [tex]10^{0.1}[/tex] = 1.29

Hence, the sound intensity will increase by a factor of 1.29.