Question

Use Mathematical Thinking On the decibel scale, a sound that is ten decibels higher is

Answer 1

The 120 dB jet plane taking off is 10⁸ times louder than a 40 dB conversation.

Since a ten decibel higher sound is ten times louder. Also, a twenty decibel sound is 100 times higher. If we go on like this, it implies that a thirty decibel sound would be 1000 times higher.

Loudness formula

So, 10 dB = 10 times

20 dB = 100 times

30 dB = 1000 times

So, it implies that the loudness would be L = $10^{\frac{dB}{10} }$.

Difference of sound level

Now to find how many more times louder than a 40-dB conversation is a 120-dB jet plane taking off.

The difference in their sound level is 120 dB - 40 dB = 80 dB.

Number of times louder

So, the number of times louder would be gotten from L = $10^{\frac{dB}{10} }$ with dB = 80.

So, L = $10^{\frac{60}{10} }$ = 10⁸

So, the 120 dB jet plane taking off is 10⁸ times louder than a 40 dB conversation.

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