Answer
See answers. Numbers may vary due to uncertainty in the reading of the graph.
Work Step by Step
a. Consult Figure 12–6. At 100 Hz, the threshold of hearing is approximately 35 dB. The threshold of pain is about 126 dB. The difference is 91 dB. Find the ratio of highest to lowest intensity, using equation 12-1.
$$91dB=10log\frac{I_{loud}}{I_{soft}}$$
$$9.1dB=log\frac{I_{loud}}{I_{soft}}$$
$$10^{9.1}= \frac{I_{loud}}{I_{soft}}\approx 1.3\times10^{9}$$
b. Consult Figure 12–6. At 5000 Hz, the threshold of hearing is approximately -5 dB. The threshold of pain is about 110 dB. The difference is 115 dB. Find the ratio of highest to lowest intensity, using equation 12-1.
$$115dB=10log\frac{I_{loud}}{I_{soft}}$$
$$11.5dB=log\frac{I_{loud}}{I_{soft}}$$
$$10^{11.5}= \frac{I_{loud}}{I_{soft}}\approx 3\times10^{11}$$
