A string fixed at both ends is 8.40 m long and has a mass of 0.120 kg . It is subjected to a ten

Name: Problem 41, Chapter 16: Fundamentals of Physics
Uploaded: 2019-12-17T00:44:36-08:00
Duration: 2 min 12 s
Channel: Kai Chen
Description: A string fixed at both ends is 8.40 m long and has a mass of 0.120 kg . It is subjected to a tension of 96.0 N and set oscillating. (a) What is the speed of the waves on the string? (b) What is the longest possible wavelength for a standing wave? (c) Give the frequency of that wave.

step 1 So in this question, we're dealing with standing waves. We have a string that is fixed on both h

Question

A string fixed at both ends is 8.40 $\mathrm{m}$ long and has a mass of 0.120 $\mathrm{kg} .$ It is subjected to a tension of 96.0 $\mathrm{N}$ and set oscillating. (a) What is the speed of the waves on the string? (b) What is the longest possible wavelength for a standing wave? (c) Give the frequency of that wave.

   A string fixed at both ends is 8.40 $\mathrm{m}$ long and has a mass of 0.120 $\mathrm{kg} .$ It is subjected to a tension of 96.0 $\mathrm{N}$ and set oscillating. (a) What is the speed of the waves on the string? (b) What is
the longest possible wavelength for a standing wave? (c) Give the
frequency of that wave.

Fundamentals of Physics

David Halliday,… 10th Edition

Chapter 16, Problem 41

Instant Answer

Solved by Expert Kai Chen

12/17/2019

Step 1

The mass density can be calculated as $\mu = \frac{m}{L}$, where $m$ is the mass of the string and $L$ is the length of the string. Show more…

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A string fixed at both ends is 8.40 $\mathrm{m}$ long and has a mass of 0.120 $\mathrm{kg} .$ It is subjected to a tension of 96.0 $\mathrm{N}$ and set oscillating. (a) What is the speed of the waves on the string? (b) What is the longest possible wavelength for a standing wave? (c) Give the frequency of that wave.

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Key Concepts

Wave Speed on a String

The speed of a transverse wave on a string is determined by the tension in the string and its mass per unit length, given by the equation v = ?(T/?). This concept explains how higher tension increases the wave speed while a larger mass per unit length decreases it.

Standing Waves and Modes

Standing waves occur on strings fixed at both ends due to the interference of waves traveling in opposite directions, leading to nodes and antinodes. Only certain wavelengths, given by the condition ? = 2L/n (where L is the length of the string and n is a positive integer), are allowed, with the fundamental (lowest) mode corresponding to n = 1.

Frequency-Wavelength Relationship

The relationship between frequency, wave speed, and wavelength is described by the equation v = f?. This is crucial for connecting the physical parameters of a wave to its temporal behavior. Once the wavelength and wave speed are determined, the frequency can be calculated as f = v/?.

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