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A wave pulse traveling to the right along the x-axis is described by the equation y(x, t) = 2.0 / ((x − 3.0t)² + 1), where x and y are measured in centimeters and t is in seconds. The peak height of the pulse is defined as the largest displacement along the y-axis. Which of the following is true?
- The peak height of the pulse decreases over time.
- The peak height of the pulse remains unchanged over time.
- The pulse moves at a speed of 3.0 cm/s.
- The pulse moves at a speed of 0.33 cm/s.
Correct answer: The peak height of the pulse remains unchanged over time.
Solution
The equation of the pulse shows that its peak height depends only on the denominator, which remains constant over time. Therefore, the peak height of the pulse does not change as it propagates.
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