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Dolphins emit clicks of sound for communication and echolocation. A marine biologist is monitoring a dolphin swimming in seawater where the speed of sound is 1522 m/s. When the dolphin is swimming directly away at 8.5 m/s, the marine biologist measures the number of clicks occuring per second to be at a frequency of 2770 Hz.
1. What is the difference (in Hz) between this frequency and the number of clicks per second actually emitted by the dolphin?

Respuesta :

cjmejiab

From Doppler effect we have that the frequency observed for the relation between the velocities is equivalent to the frequency observed. That is mathematically,

[tex]F_r = \frac{v}{v+v_s}F_s[/tex]

Here,

Speed of sound in water [tex]v = 1522m/s[/tex]

The Dolphin swims directly away from the observer with a velocity [tex]v_s = 8.5m/s[/tex]

Observed frequency of the clicks produced by the dolphin [tex]F_r = 2770Hz[/tex]

Replacing we have,

[tex]F_r = \frac{v}{v+v_s}F_s[/tex]

[tex]F_s = \frac{v+v_s}{v}[/tex]

[tex]F_s = 2770 (\frac{1522}{1522+8.5})[/tex]

[tex]F_s = 2754.61Hz[/tex]

Therefore the frequency emitted by the dolphin is 2754.61Hz

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