Question

The power of sound from the speaker of a radio is 20 milliwatt. By turning the knob of the volume control the power of the sound is increased to 400 milliwatt . The power increase in decibels as compared to the original power is

• A. 13 db
• B. 10 db
• C. 20 db
• D. 800 db

Answer 1

The correct option is A 13 db

$\begin{array}{c}P\alpha I{L}_1=10{\log }_{10}\left(\frac{I_1}{I_0}\right)and{L}_2=10{\log }_{10}\left(\frac{I_2}{I_0}\right)\\ So,\\ L_2-L_1=10{\log }_{10}\left(\frac{I_2}{I_1}\right)=10{\log }_{10}\left(\frac{P_2}{P_1}\right)\\ =10{\log }_{10}\left(\frac{400}{10}\right)\\ =10{\log }_{10}20\\ =10\log \left(2\times 10\right)\\ =10\left(0.301+1\right)\\ =13dB.\end{array}$

Hence, the option $A$ is the correct answer.