Suppose a turbine at 25,000 RPM makes a noise of 147 decibels and at 30,000 RPM makes a noise of 163 decibels. What is the ratio of the sound intensity of the turbine at 30,000 RPM to the sound intensity at 25,000 RPM?
A) 39.8
B) 63.1
C) 50.1
D) 31.6

Question

Quizplus · Accepted Answer

The sound intensity is proportional to the square of the sound pressure level. The sound pressure level is given by:$$SPL = 20 \log_{10} \left(\frac{p}{p_0}\right)$$where p is the sound pressure and p0 is the reference sound pressure (20 micropascals).The ratio of the sound intensity at 30,000 RPM to the sound intensity at 25,000 RPM is:$$\frac{I_{30,000}}{I_{25,000}} = \left(\frac{p_{30,000}}{p_{25,000}}\right)^2$$$$= \left(\frac{10^{SPL_{30,000}/20}}{10^{SPL_{25,000}/20}}\right)^2$$$$= \left(\frac{10^{163/20}}{10^{147/20}}\right)^2$$$$= 39.8$$

Suppose a Turbine at 25,000 RPM Makes a Noise of 147