How Does a Duck Help Us Understand Wave Mechanics?

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The discussion explores how a Harlequin duck's bobbing behavior illustrates wave mechanics, specifically focusing on frequency, speed, and wavelength of water waves. The duck completes 7.03 cycles in 10.4 seconds, leading to a frequency calculation of approximately 0.676 Hz. The wave speed is determined by the distance traveled by a wave crest, calculated at 1.78 m/s. The wavelength can be derived using the relationship between speed, frequency, and wavelength, resulting in a value of 2.63 m. A mathematical expression for the sinusoidal wave function is provided as (x, t) = cos(x - t), with the duck at the origin at a wave peak when t = 0 s.
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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.
 
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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?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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