Question

If the intensity level of a sound wave is increased by factor 20 the corresponding change in decibels level of the sound would be

• A. 13 dB
• B. 7 dB
• C. 19 dB
• D. 27 dB

Answer 1

Answer: (A)

As we know that, $\beta =10\log \left(\frac{I_2}{I_1}\right)$ If the actual intensity of sound is $I_0.$ Then, when the intensity is I ${\beta }_1=10\log \left(\frac{I}{I_0}\right)$ When the intensity is increased by a factor 20 Then, ${\beta }_2=10\log \left(\frac{20I}{I_0}\right)$ Thus, change in decibels of sound ${\beta }_2-{\beta }_1=10\log \left(\frac{20I}{I_0}\right)-10\log \left(\frac{I}{I_0}\right)$ $=10\log \left(\frac{20I}{I}\right)=10\log 20$ $=13dB.$