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A person wears a hearing aid that uniformly increases the sound level of all audible frequencies of sound by 30.0 dB. The hearing aid picks up sound having a frequency of 250 Hz at an intensity of 3.0×10−11 W/m2. What is the intensity delivered to the eardrum (in …×10−8 W/m2 )?

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Detailed Solution

In terms of their intensities, the difference in the decibel level of two sounds is L2−L1=(10dB)log⁡I2I0−(10dB)I1I0=(10dB)log⁡I2I0⋅I0I1=(10dB)log⁡I2I1Thus, I2I1=10L2−L1/10 or I2=I1×10β2−β1/10If L2−L1=30 dB and I1=3.0×10−11 W/m2, then I2=3.0×10−11 W/m2×103=3.0×10−8 W/m2

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A person wears a hearing aid that uniformly increases the sound level of all audible frequencies of sound by 30.0 dB. The hearing aid picks up sound having a frequency of 250 Hz at an intensity of 3.0×10−11 W/m2. What is the intensity delivered to the eardrum (in …×10−8 W/m2 )?