P18 078

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78.

(a) If the destroyer drifts with the current, then it will detect a signal with frequency f



given by

f



=

f



v

v

− u

1



=

(1000 Hz)(5470 km/h)

5470 km/h

(75.0 km/h 30.0 km/h)

=

1008.29 Hz .

Thus, ∆f = f



− f = 8.29 Hz.

(b) If the destroyer is stationary with respect to the ocean floor, then it is moving at u

2

= 30.0 km/h

relative to the current. The detected frequency then becomes

f



=

f



v + u

2

v

− u

1



=

(1000 Hz)(5470 km/h + 30.0 km/h)

5470 km/h

(75.0 km/h 30.0 km/h)

=

1013.9 Hz .

Thus, ∆f = f



− f = 13.9 Hz.


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