A transverse wave on a cable can be modeled by the equation y(x, t) = 0.364 sin(1.30x + 89.8t), where x and y are in meters and t is in seconds. Imagine the cable has a small mark on it at x = 0. (a) What is the time interval (in ms) between the first two instants when this mark has a position of y = 0.175 m? 69.92 We are interested in the first two times the mark at x = 0 reaches the desired displacement. When dealing with angles be careful with the distinction between degrees and radians. Since we are interested in the first two times the sine of an angle has a particular value, it may be helpful to recall that sin(0) = sin(-0). ms (b) What distance (in m) does the wave travel during the time interval found in part (a)? 4.83 x Check your units. How is the distance the wave travels along the cable related to the speed and time of travel? How is the speed of the wave travelling along the cable related to the angular frequency and wave number? m Need Help? Read It

Physics for Scientists and Engineers: Foundations and Connections
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ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter17: Traveling Waves
Section: Chapter Questions
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A transverse wave on a cable can be modeled by the equation
y(x, t) = 0.364 sin(1.30x + 89.8t),
where x and y are in meters and t is in seconds. Imagine the cable has a small mark on it at x = 0.
(a) What is the time interval (in ms) between the first two instants when this mark has a position of y = 0.175 m?
69.92
x
We are interested in the first two times the mark at x = reaches the desired displacement. When dealing with angles be careful with the distinction between degrees and radians. Since we are
interested in the first two times the sine of an angle has a particular value, it may be helpful to recall that sin(0) = sin(-0). ms
(b) What distance (in m) does the wave travel during the time interval found in part (a)?
4.83
x
Check your units. How is the distance the wave travels along the cable related to the speed and time of travel? How is the speed of the wave travelling along the cable related to the angular
frequency and wave number? m
Need Help?
Read It
Transcribed Image Text:A transverse wave on a cable can be modeled by the equation y(x, t) = 0.364 sin(1.30x + 89.8t), where x and y are in meters and t is in seconds. Imagine the cable has a small mark on it at x = 0. (a) What is the time interval (in ms) between the first two instants when this mark has a position of y = 0.175 m? 69.92 x We are interested in the first two times the mark at x = reaches the desired displacement. When dealing with angles be careful with the distinction between degrees and radians. Since we are interested in the first two times the sine of an angle has a particular value, it may be helpful to recall that sin(0) = sin(-0). ms (b) What distance (in m) does the wave travel during the time interval found in part (a)? 4.83 x Check your units. How is the distance the wave travels along the cable related to the speed and time of travel? How is the speed of the wave travelling along the cable related to the angular frequency and wave number? m Need Help? Read It
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