Question

how many times more intense is 20 dB sound compared to 10dB sound.
1) 10time 2) 1/10 time. 3) 1/2 time. 4) 2 time.

Answer 1

Answer on Question 51587, Physics, Mechanics | Kinematics | Dynamics

Question:

How many times more intense is 20dB sound compared to 10dB sound?

1) 10 times

2) 1/10 times

3) 1/2 times

4) 2 times

Solution:

In order to answer this question we use the decibel formula for comparison of sound power level:

$$I_{dB} = 10 \log_{10} \frac{P}{P_0}$$

where, $I_{dB}$ is the intensity in decibels, $P$ is the intensity of a sound source and $P_0$ is the measure of known intensity (the threshold of hearing for example).

Let us rearrange our formula:

$$\frac{I_{dB}}{10} = \log_{10} \frac{P}{P_0}$$ $$10^{\left(\frac{I_{dB}}{10}\right)} = \frac{P}{P_0}$$

So, for the 20dB sound we have:

$$10^{\left(\frac{20}{10}\right)} = 100 = \frac{P_{20}}{P_0}$$

And for the 10dB sound we have:

$$10^{\left(\frac{10}{10}\right)} = 10 = \frac{P_{10}}{P_0}$$

Finally we obtain $\frac{P_{20}}{P_{10}} = \frac{100}{10} = 10$ , therefore $20dB$ sound is 10 times intense compared to $10dB$ sound.

**Answer:**

1) 10 times

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