20. **Understanding Sinusoidal Waves and Power Calculation**The image above features a graph illustrating a sinusoidal wave in a string. Below the graph, the power formula for this wave, which defines the rate at which it transports energy, is presented:\[ P = b \cdot A^2 \]where:- \( b \) is the proportionality constant- \( A \) is the amplitude### Graph DescriptionThe graph shows a sinusoidal wave plotted against position (in centimeters). The horizontal axis (x-axis) represents the position \( x \) in centimeters, ranging from -10 cm to 10 cm. The vertical axis represents the displacement of the wave, ranging from -20 to 20 units. The wave oscillates smoothly above and below the zero displacement line, depicting the characteristic shape of a sine wave.### Power of a Sinusoidal WaveAccording to the presented formula, the power \( P \) of this sinusoidal wave is directly proportional to the square of its amplitude \( A \). In other words, as the amplitude increases, the power increases quadratically.### Example CalculationLet's consider the given example:- The proportionality constant \( b \) is given as \( 7100 \, \text{W/m}^2 \).To calculate the power of the wave, we need to ascertain the amplitude \( A \) from the graph and then apply the formula:1. **Estimate the Amplitude (A)**: The amplitude is the maximum displacement from the central axis (zero line) to the peak of the wave. In this case, the wave appears to reach around 15 units at its peaks. \( A \approx 15 \, \text{cm} \)2. **Apply the Formula**:\[ P = 7100 \cdot (15)^2 \]\[ P = 7100 \cdot 225 \]\[ P = 1,597,500 \, \text{W/m}^2 \]### ConclusionUnderstanding the relationship between amplitude and power is crucial in wave mechanics. This graph and formula demonstrate how even small changes in amplitude can lead to significant differences in the energy transported by the wave. This calculation method can be particularly useful in educational scenarios to help students grasp these fundamental physics principles.

Given Rate of energy transmitted through string P = b.A2 where , b = 7100 w/m2 & Amplitude…

15 10 5 x (cm) WM A 0 -10 -5 10 -5/ 10 -15 -20 P = b. A² b = proportionality constant A = amplitude The graph above shows a snapshot of a sinusoidal wave in a string. As shown in the formula (also above), the power of this wave (the rate at which it transports energy) is directly proportional to the square of the amplitude of the wave. If b = 7100 W/m², then calculate the power of the wave. (Note. This calculation estimates the amplitude to a tenth of a centimeter.)

15 10 5 x (cm) WM A 0 -10 -5 10 -5/ 10 -15 -20 P = b. A² b = proportionality constant A = amplitude The graph above shows a snapshot of a sinusoidal wave in a string. As shown in the formula (also above), the power of this wave (the rate at which it transports energy) is directly proportional to the square of the amplitude of the wave. If b = 7100 W/m², then calculate the power of the wave. (Note. This calculation estimates the amplitude to a tenth of a centimeter.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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