## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 12 - Problems - Page 465: 51

#### Answer

(a) The distance to one side of the fjord is $668~m$ (b) The captain will hear the second echo 2.78 seconds after hearing the first echo.

#### Work Step by Step

(a) We can find the speed of sound at a temperature of $5.0^{\circ}C$: $v = 331+0.6~T$ $v = 331+(0.6)(5.0^{\circ}C)$ $v = 334~m/s$ We can find the distance the sound travels in a time of 4.0 seconds: $d = v~t = (334~m/s)(4.0~s) = 1336~m$ Since the echo traveled to the side of the fjord and back to the ship, the distance to one side of the fjord is $\frac{1336~m}{2}$ which is $668~m$ (b) We can find the distance to the other side of the fjord: $d' = 1800~m - 668~m = 1132~m$ For the sound to reach the other side of the fjord and come back to the ship as an echo, the sound must travel a distance of $(2)(1132~m)$ which is $2264~m$. We can find the time for the sound to travel this distance: $t = \frac{2264~m}{334~m/s} = 6.78~s$ The captain hears the first echo after 4.0 seconds. Therefore, the captain will hear the second echo 2.78 seconds after hearing the first echo.

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