Unformatted text preview: Physics 7 C Quiz 1
First Name Last Name ID Section A one dimensional wave traveling on a 50 cm long piece of rope is observed to have the following y(x) and y(t) graphs.
The y(x) graph is at time t = 0 seconds and the y(t) graph is at position x = 15 cm. y(z), cm, at t = 0 s y(t), cm, at x = 15 cm cc, cm a). If, on this same 50 cm piece of rope, you were to excite a new wave that had the same ﬁxed phase constant ([50, same
amplitude A, and same equilibrium position yo, but traveled in the opposite direction and had a frequency half that
of the wave pictured above, what equation y(x,t) would describe this new wave? From the y(x) graph, we can see the wavelength of the depicted wave is 30 cm. From the y(t) graph, we can see
the period of the depicted wave is four seconds. Since the wave we want to describe has a frequency half that the
original wave, the period of the new wave must be twice that of the old wave, as period is the inverse of frequency.
Since the medium (i.e., the rope) is the same for both waves, 2} = /\ f is the same as well, leading us to conclude that
the new wavelength must also be twice the old one. From either graph, we can observe that since the function is
oscillating between +3 cm and -2 cm, the amplitude A = 2.5 cm while the equilibrium position yo = 0.5 cm. These are
both the same for the new wave. To ﬁnd the direction the wave is traveling, we observe that at the point in common
(t = 0 s, x = 15 cm), the y(t) graph is decreasing, which is consistent with the y(x) graph traveling to the right.
Hence, the new wave will travel to the left. Finally, observe that there is a minimum at :1: = 15 cm, t = 1 s, so for the oldwave 1 15
71' 71' 71' This is the same in the new wave, so we get in all for our new wave . t a:
y(m,t) — (2.5 cm) s1n (27rﬁ + 2160 cm ) + 0.5 cm (2) b). On the graph provided below, plot y(x) at time t = 0 seconds for this new wave on the 50 cm long rope.
y(m), cm, at t = 0 s This plot follows directly if one sets t = 0 in equation 2 above. Fun facts: 1) = Af, f = %, y(m,t) = Asin (21% :: 2n? + 450) +310 ...
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- Spring '08