How Does a Duck Help Us Understand Wave Mechanics?

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SUMMARY

The discussion focuses on understanding wave mechanics through the behavior of a Harlequin duck (Histrionicus histrionicus) in response to water waves. The duck bobs vertically 10.0 cm over 7.03 cycles in 10.4 seconds, leading to a calculated wave frequency of 0.676 Hz and a wave speed of 1.78 m/s. The wavelength is determined using the relationship between speed, frequency, and wavelength, resulting in a wavelength of approximately 2.63 m. The mathematical expression for the sinusoidal wavefunction is given as (x, t) = cos(x - t).

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Duck season has arrived. A Harlequin duck (Histrionicus histrionicus) is bobbing vertically up and down due to a passing water wave. The duck bobs through a total vertical distance of 10.0 cm and completes 7.03 cycles during 10.4 s according to your Mickey Mouse watch. You also note that a particular crest of the wave travels the 8.99 m from the duck to your canoe during 5.05 s.

(a) What is the frequency of the water wave?
Hz
(b) What is the speed of the wave?
m/s
(c) What is the wavelength of the waves?
m
(d) Write a mathematical expression for the wavefunction (x, t) assuming it is a sinusoidal wave with the duck located at the origin for x and at a peak of the wave when t = 0 s.
(x, t) = cos( x - t)


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Please explain as well, don't just calculate. Thanks.
 
Physics news on Phys.org
You are given so many cycles in so many seconds. What's that number in units of cycles per second?

You are given so many meters in so many seconds. What's that number in units of meters per second?

What vocabulary words are the names of the above variables?

What formula relates them to the wavelength?
 

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