Question

You are in a boat traveling perpendicular to waves in water. The wave speed is 8.20 m/s, your speed is 6.80 m/s, and you are heading into the waves. If the wavelength of the waves is 8.20 m, how much time passes between hitting the top of one wave and the next? [This Doppler effect in water is just like that in sound; you can also calculate it from velocities and length.] __________ s

Answer 1

Let us fnd out the time between one wave and the next,

first, if we are at rest, the period of the wave is given by

T= lambda/V_w=8.2 m/8.2(m/s)=1.0 s

now, if we are heading into the waves, the period is given by

T= lambda/(V_w+V)=8.2 m/15.0(m/s)= 0.5467 S

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We can also apply,

F*=F(1+V_o/V_w)

where,

V_o=6.8 m/s

V_w=8.2 m/s

F=V_w/lambda=8.2/8.2 =1.0 Hz

F*= 1.8293 Hz

and

T*=1/F*= 0.5467 s

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