wo transverse waves travel along the same taut string and interfere. Waves 1 and 2 are described, respectively, by the function y1(x, t) = A sin(kx - ωt) and y2(x, t) = A cos(3kx + 3ωt). The phases (arguments of the sine and cosine functions) are in radians, as usual, and A = 7.9 cm, k = 5.1 rad/m, ω = 3.2 rad/s. a. In what direction does each wave travel? Wave 1 travels in the negative x-direction, while wave 2 travels in the positive x-direction. There is not enough information. Wave 1 travels in the positive x-direction, while wave 2 travels in the negative x-direction. Because wave 2 is described using a cosine, it does not travel. Wave 1 travels in the negative x-direction. Because wave 1 is described using a sine, it does not travel. Wave 2 travels in the negative x-direction. Both waves travel in the positive x-direction. Both waves travel in the negative x-direction.
Interference of sound
Seiche
A seiche is an oscillating standing wave in a body of water. The term seiche pronounced saysh) can be understood by the sloshing of water back and forth in a swimming pool. The same phenomenon happens on a much larger scale in vast bodies of water including bays and lakes. A seizure can happen in any enclosed or semi-enclosed body of water.
Two transverse waves travel along the same taut string and interfere. Waves 1 and 2 are described, respectively, by the function y1(x, t) = A sin(kx - ωt) and y2(x, t) = A cos(3kx + 3ωt). The phases (arguments of the sine and cosine functions) are in radians, as usual, and A = 7.9 cm, k = 5.1 rad/m, ω = 3.2 rad/s.
a. In what direction does each wave travel?
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b.
Which option correctly describes wave 2 as a sine wave? | ||||||||||
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c.
Use the trigonometric identity to find the correct total wave function for the interfering waves on the string. | ||||||||
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d. For A = 7.9 cm, k = 5.1 rad/m, and ω = 3.2 rad/s, calculate the total displacement of the string, in centimeters, at the position x = 3.8 m at time t = 8.2 s. y=
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