You are walking next to a large lake, and notice there are traveling waves movin

Question

You are walking next to a large lake, and notice there are traveling waves moving across the lake, driven by the wind. You want to know how fast they're traveling, but it's tricky to estimate directly. Then you spot a duck bobbing up and down in the water about 30 m away from you. Being a sound and music student, you make some quick visual estimates: you see that the duck bobs up and down about once every 7.0 seconds. It is bobbing a total vertical distance of about 0.5 m up and down (from peak to trough.) You also see that when the duck is at a peak there is about 6.0 meters between it and the next peak. You guess the water temperature is about 15 oC, and air temperature is about 25 oC. How fast are the waves traveling? (Find your answer in m/s, but do not enter units.)

Explanation / Answer

The wavelength is the peak to peak distance which is 6 m(given)

so lamda = 6 m.

The time interval between up and down and then up is the time period which is 7 sec(given)

So T= 7s.

Now the velocity of the wave is the ratio of wavelength and time period,

so velocity v= 6/7 = 0.86 m/s

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