Low-frequency vertical oscillations are one possible cause of motion sickness, with 0.30 Hz having the strongest effect. Your boat is bobbing in place at just the right frequency to cause you the maximum discomfort. The water wave that is bobbing the boat has crests that are 30 m apart. What will be the boat’s vertical oscillation frequency if you drive the boat at 5.0 m/s in the direction of the oncoming waves?.

The answer to the question is;

The boat’s vertical oscillation frequency if you drive the boat at 5.0 m/s in the direction of the oncoming waves moving at 9 m/s in the opposite direction is  0.467 Hz.

Explanation:

We note the frequency of the water wave = 0.3 Hz

Distance between crests or wavelength of water wave  = 30 m

Speed v of a wave is given by Frequency f × Wavelength λ

Therefore the speed of the wave = f·λ = 0.3 × 30 = 9 m/s

(b)  Distance between crests = 30 m = wavelength λ

     Boat speed                       = 5.0 m/s v

Speed of the wave with respect to the boat = 5 + 9 = 14 m/s

From the wave speed relationship, we have

v = fλ    f = = = 0.467 Hz which is high.

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