The ratio of intensities between two coherent | vedclass

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(A) Given the ratio of intensities $I_1/I_2 = 4/1$,so $I_1 = 4I_2$.Let the amplitudes be $A_1$ and $A_2$. Since $I \propto A^2$,we have $A_1/A_2 = \sq

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$20 \log_{10}(3)$

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(A) Given the ratio of intensities $I_1/I_2 = 4/1$,so $I_1 = 4I_2$.Let the amplitudes be $A_1$ and $A_2$. Since $I \propto A^2$,we have $A_1/A_2 = \sqrt{I_1/I_2} = \sqrt{4/1} = 2/1$,so $A_1 = 2A_2$.The maximum intensity is $I_{max} = (A_1 + A_2)^2 = (2A_2 + A_2)^2 = (3A_2)^2 = 9A_2^2$.The minimum intensity is $I_{min} = (A_1 - A_2)^2 = (2A_2 - A_2)^2 = (A_2)^2 = A_2^2$.The ratio of maximum to minimum intensity is $I_{max}/I_{min} = 9/1$.The difference in loudness $\Delta L$ in $dB$ is given by $\Delta L = 10 \log_{10}(I_{max}/I_{min})$.Substituting the values,$\Delta L = 10 \log_{10}(9) = 10 \log_{10}(3^2) = 20 \log_{10}(3)$.

The ratio of intensities between two coherent sound sources is $4:1$. The difference of loudness in $dB$ between maximum and minimum intensities when they interfere in the space is ..........

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