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A middle-aged man typically has poorer hearing than a middle-aged woman. In one case a woman can just begin to hear a musical tone, while a man can just begin to hear the tone only when its intensity level is increased by 9.4 dB relative to the just-audible intensity level for the woman. What is the ratio of the sound intensity just detected by the man to the sound intensity just detected by the woman? (level just detected by man / level just detected by woman)

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Answer:

8.7

Explanation:

[tex]I_m[/tex] = Intensity of sound heard by man

[tex]I_w[/tex] = Intensity of sound heard by woman

[tex]\beta[/tex] = Intensity indecibels = 9.4 dB

Intensity of sound is given by

[tex]\beta=10log\frac{I_m}{I_w}\\\Rightarrow \frac{\beta}{10}=log\frac{I_m}{I_w}\\\Rightarrow 10^{\frac{\beta}{10}}=\frac{I_m}{I_w}\\\Rightarrow \frac{I_m}{I_w}=10^{\frac{9.4}{10}}\\\Rightarrow \frac{I_m}{I_w}=8.7[/tex]

So, the ratio of sound intensity by the man to the sound intensity just detected by the woman is 8.7

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