Chapter 17

0.288 m

332 m/s

0.223

(a) 7.70 m

(b) This means that sonar is good for spotting and locating large objects, but it isn’t able to resolve smaller objects, or detect the detailed shapes of objects. Objects like ships or large pieces of airplanes can be found by sonar, while smaller pieces must be found by other means.

(a) 18.0 ms, 17.1 ms

(b) 5.00%

(c) This uncertainty could definitely cause difficulties for the bat, if it didn’t continue to use sound as it closed in on its prey. A 5% uncertainty could be the difference between catching the prey around the neck or around the chest, which means that it could miss grabbing its prey.

106 dB

(a) 93 dB

(b) 83 dB

(a) 50.1

(b) $5.01\times {10}^{\mathrm{–3}}$ or $\frac{1}{200}$

70.0 dB

100

28.2 dB

(a) 878 Hz

(b) 735 Hz

(a) 12.9 m/s

(b) 193 Hz

First eagle hears $4.23\times {10}^3\text{Hz}$

Second eagle hears $3.56\times {10}^3\text{Hz}$

0.7 Hz

0.3 Hz, 0.2 Hz, 0.5 Hz

(a) 256 Hz

(b) 512 Hz

180 Hz, 270 Hz, 360 Hz

1.56 m

(a) 0.334 m

(b) 259 Hz

3.39 to 4.90 kHz

(a) 367 Hz

(b) 1.07 kHz

(a) $f_n=n\left(\mathrm{47.6\; Hz}\right),n=\mathrm{1,\; 3,\; 5,...,\; 419}$

(b) $f_n=n\left(\mathrm{95.3\; Hz}\right),n=\mathrm{1,\; 2,\; 3,...,\; 210}$

498.5 or 501.5 Hz

82 dB

approximately 48, 9, 0, –7, and 20 dB, respectively

(a) 23 dB

(b) 70 dB

Five factors of 10

(a) $2\times {\text{10}}^{-\text{10}}{\text{W/m}}^2$

(b) $2\times {\text{10}}^{-\text{13}}{\text{W/m}}^2$

2.5

1.26

170 dB

103 dB

(a) 1.00

(b) 0.823

(c) Gel is used to facilitate the transmission of the ultrasound between the transducer and the patient’s body.

(a) $\mathrm{77.0\; \mu m}$

(b) Effective penetration depth = 3.85 cm, which is enough to examine the eye.

(c) $\mathrm{16.6\; \mu m}$

(a) $5.78\times {10}^{\mathrm{–4}}\text{m}$

(b) $2.67\times {10}^6\text{Hz}$

(a) $v_{\mathrm{w}}=\mathrm{1540\; m/s}=\mathrm{f\lambda }\Rightarrow \lambda =\frac{\mathrm{1540\; m/s}}{100\times {10}^3\text{Hz}}=\mathrm{0.0154\; m\; <\; 3.50\; m.}$ Because the wavelength is much shorter than the distance in question, the wavelength is not the limiting factor.

(b) 4.55 ms

974 Hz

(Note: extra digits were retained in order to show the difference.)