First slide

Charaterstics of sound

Question

The difference of sound levels between two points is 30 dB. The ratio of pressure amplitude between the two points is

Moderate

A

10
B

20
C

30
D

32

Solution

Here
$L_{1} = 10 \log_{10} (\frac{I_{1}}{I_{0}}) and L_{2} = 10 \log_{10} (\frac{I_{2}}{I_{0}}) ΔL = L_{2} - L_{1} = 10 \log_{10} (\frac{I_{2}}{I_{1}}) = 10 \log_{10} {(\frac{P_{2}}{P_{1}})}^{2} (∵ I \propto P^{2}) Now 30 = 20 \log_{10} (\frac{P_{2}}{P_{1}}) or \frac{3}{2} = \log_{10} (\frac{P_{2}}{P_{1}}) or \frac{P_{2}}{P_{1}} = (10)^{3 / 2} - \sqrt{(1000)} = 31 \cdot 62 \approx 32$

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