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[74]
The loudness of a whisper is $20 dB$ , and that of a conversation is $60 dB$ . How many times is the sound of the conversation louder than a whisper?

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100 times

1000 times

10000 times

100000 times

answer is C.

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Detailed Solution

The loudness of a whisper is

20 dB

, and that of a conversation is

60 dB

. The sound of the conversation louder than a whisper is

10000 times

.
Loudness of sound,

L = 10 \log_{10} \frac{I}{I_{0}}

Where

L

is loudness and

I

is intensity.

I_{1} = Intensity of Whisper and I_{2} = Intensity of conversation

We get,

L_{2} - L_{1} = 10 \log_{10} \frac{I_{2}}{I_{1}}

Given :

L_{1} = 30 dB  and L_{2} = 60 dB

60 - 30 = 10 \log_{10} \frac{I_{2}}{I_{1}}

\Rightarrow \log_{10} \frac{I_{2}}{I_{1}} = 3

\Rightarrow \frac{I_{2}}{I_{1}} = 1 0^{3}

\Rightarrow I_{2} = 1000 I_{1}

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