$\begin{array}{lll}{v}_{\text{w}}& =& (\text{331 m/s})\sqrt{\frac{T}{\text{273 K}}}=(\text{331 m/s})\sqrt{\frac{\text{293 K}}{\text{273 K}}}\\ & =& \text{343 m/s}\end{array}$

(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.

First eagle hears $4.23\times {10}^{3}\phantom{\rule{0.25em}{0ex}}\text{Hz}$

Second eagle hears $3.56\times {10}^{3}\phantom{\rule{0.25em}{0ex}}\text{Hz}$

(a) ${f}_{n}=n\left(\mathrm{47.6\; Hz}\right),\phantom{\rule{0.25em}{0ex}}n=\mathrm{1,\; 3,\; 5,...,\; 419}$

(b) ${f}_{n}=n\left(\mathrm{95.3\; Hz}\right),\phantom{\rule{0.25em}{0ex}}n=\mathrm{1,\; 2,\; 3,...,\; 210}$

(a) $2\times {\text{10}}^{-\text{10}}\phantom{\rule{0.25em}{0ex}}{\text{W/m}}^{2}$

(b) $2\times {\text{10}}^{-\text{13}}\phantom{\rule{0.25em}{0ex}}{\text{W/m}}^{2}$

(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) $5.78\times {10}^{\mathrm{\u20134}}\phantom{\rule{0.25em}{0ex}}\text{m}$

(b) $2.67\times {10}^{6}\phantom{\rule{0.25em}{0ex}}\text{Hz}$

(a) ${v}_{\mathrm{w}}=\mathrm{1540\; m/s}=\mathrm{f\lambda}\Rightarrow \lambda =\frac{\mathrm{1540\; m/s}}{100\times {10}^{3}\phantom{\rule{0.25em}{0ex}}\text{Hz}}=0.0154m<3.50m.$ Because the wavelength is much shorter than the distance in question, the wavelength is not the limiting factor.

(b) 4.55 ms

Answers vary. Students could include a sketch showing an increased amplitude when two waves occupy the same location. Students could also cite conceptual evidence such as sound waves passing through each other.

Striking the end of a protruding ruler would create transverse waves, not sound waves. Any measurable, audible sound would come from the repetitive striking of the ruler against the desk. The student is confused about the speed of sound through solids versus the speed of sound in air.