A) \[3dB\]
B) \[2dB\]
C) \[6dB\]
D) \[12dB\]
Correct Answer: C
Solution :
Intensity at A, \[{{I}_{A}}=\frac{P}{4\pi {{r}^{2}}};\] intensity at B, \[{{I}_{B}}=\frac{P}{4\pi \,{{(2r)}^{2}}}\] |
Sound level at A, \[{{S}_{A}}=10\log \frac{{{I}_{A}}}{{{I}_{0}}}\] |
Sound level at B, \[{{S}_{B}}=10\log \frac{{{I}_{B}}}{{{I}_{0}}}\] |
Difference of sound level at A and B is \[{{S}_{A}}-{{S}_{B}}=10\log \frac{{{I}_{A}}}{{{I}_{0}}}-10\log \frac{{{I}_{B}}}{{{I}_{0}}}=10\log \left( \frac{{{I}_{A}}}{{{I}_{B}}} \right)\] |
\[=10\log 4=20\log 2\approx 6\,dB\] |
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