Standing Waves: Finding the number of antinodes

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SUMMARY

The discussion centers on the behavior of standing waves in a string under varying tension. Initially, a string exhibits 4 antinodes at tension T1. Upon increasing the tension to T2, the correct number of antinodes in the new standing wave configuration is determined to be 5. This conclusion is based on the principle that increasing the tension results in an increase of antinodes by one, rather than doubling them.

PREREQUISITES
  • Understanding of standing wave theory
  • Knowledge of wave frequency and tension relationships
  • Familiarity with the concept of antinodes in wave mechanics
  • Basic grasp of harmonic frequencies in strings
NEXT STEPS
  • Study the relationship between tension and frequency in string vibrations
  • Learn about harmonic series in standing waves
  • Explore the mathematical derivation of antinode counts in various tensions
  • Investigate practical applications of standing waves in musical instruments
USEFUL FOR

Physics students, educators, and anyone interested in wave mechanics and the behavior of strings under tension will benefit from this discussion.

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Homework Statement



A string with a fixed frequency vibrator at one end forms a standing wave with 4 antinodes when under tension T1. When the tension is slowly increased, the standing wave disappears until tension T2 is reached with no resonances occurring between the two tensions. How many antinodes are there in this new standing wave?

Homework Equations


The Attempt at a Solution



There would be 8 antinodes, right? Because as you jump up to the next frequency, the number of antinodes doubles.

Actually, no, it would be 5 antinodes, right?
 
Last edited:
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I believe it would be 5 antinodes. Going from a given resonant tension to the next increases the number of antinodes by one.
 

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