Find Minimum Frequency to Establish Standing Wave on Wire

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SUMMARY

The discussion centers on calculating the minimum frequency required to establish a standing wave on a wire that is 1.7 meters long and has a wave speed of 587 m/s. The correct approach involves using the formula for wave speed, which is the product of frequency and wavelength. The minimum frequency corresponds to the fundamental frequency, which is determined by the longest wavelength that fits within the length of the wire, specifically half the length of the wire. Thus, the minimum frequency is 173.5 Hz.

PREREQUISITES
  • Understanding of wave mechanics, specifically standing waves
  • Familiarity with the wave speed formula: wave speed = frequency × wavelength
  • Knowledge of fundamental frequency and harmonics in physics
  • Basic algebra for solving equations
NEXT STEPS
  • Study the relationship between frequency, wavelength, and wave speed in more detail
  • Learn about harmonics and how they apply to standing waves on strings
  • Explore practical applications of standing waves in musical instruments
  • Investigate the effects of tension and mass per unit length on wave speed in strings
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators looking for examples of standing waves in practical scenarios.

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Homework Statement


A student wants to establish a standing wave on a wire 1.7 m long clamped at both ends.
The wave speed is 587 m/s. What is the minimum frequency she should apply to set up standing waves?


Homework Equations


Not sure...need help here? :)


The Attempt at a Solution


I tried 587 / 1.7 which is 345. 294
 
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Hi physicsya,

physicsya said:

Homework Statement


A student wants to establish a standing wave on a wire 1.7 m long clamped at both ends.
The wave speed is 587 m/s. What is the minimum frequency she should apply to set up standing waves?


Homework Equations


Not sure...need help here? :)

What simple formula has wave speed and frequency in it?

The Attempt at a Solution


I tried 587 / 1.7 which is 345. 294

This is close, in that you have found one of the frequencies of a standing wave. It's just not the minimum frequency.

For a string that is 1.7m long and clamped at both ends, what is the longest wavelength for a standing wave? (It is not 1.7m.)
 

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