GO In the double-slit experiment of Fig. 35-10. ihe electric fields of the waves arriving at point P are given by E 1 = (2.00 μV/m) sin[(1.26 X 10 15 ) t ] E 2 = (2.00 μV/m) sin[(1.26 X 10 15 ) t + 39, 6 rad], where time t is in seconds, (a) What is the amplitude of the resultant electric field at point P ? (b) What is the ratio of the intensity I P at point P to the intensity I cen at the center of the interference pattern? (c) Describe where point P is in the interference pattern by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies. In a phasor diagram of the electric fields, (d) at what rate would the phasors rotate around the origin and (e) what is the angle between the phasors?
GO In the double-slit experiment of Fig. 35-10. ihe electric fields of the waves arriving at point P are given by E 1 = (2.00 μV/m) sin[(1.26 X 10 15 ) t ] E 2 = (2.00 μV/m) sin[(1.26 X 10 15 ) t + 39, 6 rad], where time t is in seconds, (a) What is the amplitude of the resultant electric field at point P ? (b) What is the ratio of the intensity I P at point P to the intensity I cen at the center of the interference pattern? (c) Describe where point P is in the interference pattern by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies. In a phasor diagram of the electric fields, (d) at what rate would the phasors rotate around the origin and (e) what is the angle between the phasors?
GO In the double-slit experiment of Fig. 35-10. ihe electric fields of the waves arriving at point P are given by
E1 = (2.00 μV/m) sin[(1.26 X 1015)t]
E2 = (2.00 μV/m) sin[(1.26 X 1015)t + 39, 6 rad],
where time t is in seconds, (a) What is the amplitude of the resultant electric field at point P? (b) What is the ratio of the intensity IP at point P to the intensity Icen at the center of the interference pattern? (c) Describe where point P is in the interference pattern by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies. In a phasor diagram of the electric fields, (d) at what rate would the phasors rotate around the origin and (e) what is the angle between the phasors?
Sources A and B emit long-range radio waves of wavelength 380 m, with the phase of the emission from A ahead of that from source B by 90°. The distance rA from A to a detector is greater than the corresponding distance rB from B by 140 m. What is the magnitude of the phase difference at the detector?
Assuming that Eq. 37-36 holds, find how fast you would have to go through a red light to have it appear green. Take 620 nm as the wavelength of red light and 540 nm as the wavelength of green light.
Y(x, t) = y(x)e-it = (Aeikx + Be-ikx) e-iant
= Aei(kx-ot) + Be-i(kx+at),
(38-25)
13 In Eq. 38-25 keep both terms, putting A = B = yo. The equa-
tion then describes the superposition of two matter waves of equal
amplitude, traveling in opposite directions. (Recall that this is the
condition for a standing wave.) (a) Show that P(x, t)2 is then
given by
(x, t)² = 2y[1 + cos 2kx].
(b) Plot this function, and demonstrate that it describes the square
of the amplitude of a standing matter wave. (c) Show that the
nodes of this standing wave are located at
where n = 0, 1, 2, 3, ...
1) (1/₁).
x = (2n + 1)
and is the de Broglie wavelength of the particle. (d) Write a simi-
lar expression for the most probable locations of the particle.
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