Normal conversation has a sound level of about 60 dB. How many times more intense must a 10,000-Hz sound be compared to a 1000-Hz sound to b

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Normal conversation has a sound level of about 60 dB. How many times more intense must a 10,000-Hz sound be compared to a 1000-Hz sound to be perceived as equal to 60 phons of loudness

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6 months 2021-07-18T00:00:26+00:00 1 Answers 10 views 0

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    2021-07-18T00:01:59+00:00

    Answer: A 10,000-Hz sound is 10 times more intense as compared to a 1000-Hz sound to be perceived as equal to 60 phons of loudness.

    Explanation:

    The formula used is as follows.

    \beta = 10 dB log (\frac{I}{I_{o}})\\60 = 10 dB log (\frac{I}{I_{o}})

    I_{o} = 10^{-12} normal threshold

    The difference is sound level is as follows.

    60 – 60 = 0

    Hence,

    0 = 10 dB [log (\frac{I_{f}}{I_{o}}) - log (\frac{I_{i}}{I_{o}})]\\log (\frac{1000}{I_{o}}) = log (\frac{10000 x}{I_{o}})\\log (10^{15}) = log (10^{16}x)\\15 = 16 + log x\\log x = 1\\x = 10

    This means that 10,000 Hz sound is 10 times more intense.

    Thus, we can conclude that a 10,000-Hz sound is 10 times more intense as compared to a 1000-Hz sound to be perceived as equal to 60 phons of loudness.

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