Putting Everything Together (Exam-Type Question): A very wavy rope (2 pts). A pe

Question

Putting Everything Together (Exam-Type Question): A very wavy rope (2 pts). A person with a very nice hat shakes a long rope to make a transverse traveling wave as shown. The graph on the right is a zoomed-in snapshot of the beginning of the rope at time 0. The waveform travels down the rope to the right at a speed of v 1.8 m/s. Even though the wave is a little bit irregular, we will approximate it as a sinusoid. 2. y (cm) I0 15 20 At what frequency fis the person shaking the rope up and down? Calculate the wave number k and angular frequency ? of the transverse wave. a) Write an equation for the vertical displacement y of the rope as a function of position x (distance from the shaker's hand) and time , in the form y(x, ,)-A sin(kx ± ox-0). Give the numerical values (with correct units) of all of the constants in your equation b)

Explanation / Answer

We need wavelength which can be calculated from graph by measuring the distance between crest to crest. As the given wave in non uniform, it is difficult to find exact wavelenght, but it is approx (2 - 1.2) = 0.8 m

so, frequency of wave = speed * wavelength

f = 1.8 / 0.8 = 2.25 Hz

wave number = 2*pi / wavelength

wavenumber = 7.854 m-1

so, angular frequency = 2*pi*f

angular frequency = 14.137 rad/sec

Now we have all the values, just write down the equation

remember, A is the amplitude which is 13 cm or 0.13 m

so, Y = 0.13 sin ( 7.854x - 14.137t )

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