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Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 years ago

Logarithmic question using decibels?

Restaurant conversation is about 45 dB. If ordinary conversation is 100 times greater than restaurant conversation, how loud is ordinary conversation?

Using the formula: L = 10log (I/I0) for decibels.

Could someone show me step by step how to solve this so I can learn how? Thank you!

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  • 4 years ago
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    L = 10 log (I/Io)

    where L = loudness, I = intensity and Io is a reference intensity level.

    Let the intensity of restaurant conversation = Ir and of ordinary conversation = Ioc

    45 = 10 log (Ir/Io)

    log (Ir/Io) = 4.5

    Ir/Io = 10^4.5

    Ir = Io * 10^4.5

    Ioc = 100 * Io * 10^4.5 = Io * 10^6.5

    Ioc/Io = 10^6.5

    The loudness of ordinary conversation = 10 log (Ioc/Io)

    = 10 log (10^6.5)

    = 10 * 6.5

    = 65

    Note: The letters o, r and oc are subscripts.

    Io is the intensity when L = 0.

    If I = Io then L = 10 log (Io/Io) = 10 log 1 = 10 * 0 = 0

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