/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 29 A rope with \(280 \mathrm{g}\) o... [FREE SOLUTION] | 91影视

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Chapter 14: Problem 29

A rope with \(280 \mathrm{g}\) of mass per meter is under \(550-\mathrm{N}\) tension. Find the average power carried by a wave with frequency \(3.3 \mathrm{Hz}\) and amplitude \(6.1 \mathrm{cm}\) propagating on the rope.

Short Answer

Expert verified
The average power carried by the wave on the rope is calculated using the given parameters and the specific formula for wave power.

Step by step solution

01

Calculation of Wave Speed

First, calculate the wave speed using the formula: \( v = \sqrt{\frac{T}{\mu}} \). Substitute the given values into the equation. The tension, T = 550 N and the linear density, \( \mu \) = 0.28 kg/m. So, \( v = \sqrt{\frac{550}{0.28}} \). Evaluate the expression to obtain the wave speed.
02

Calculation of Wave Power

Next, calculate the average power carried by the wave using the formula \( P = \frac{1}{2}\mu v f^{2} A^{2} \). Substitute the known values into the equation. So, \( P = \frac{1}{2}*0.28*v*(3.3)^2*(0.061)^2 \). Evaluate the expression to find the average power carried by the wave.

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