Find New Frequency When Length AND Diameter Is Decreased?

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SUMMARY

The problem involves calculating the new frequency of a string when its length, diameter, and tension are altered. Initially, a string of length 60 cm and diameter 0.80 mm under a tension of 64 N emits a frequency of 660 Hz. When the length is decreased to 40 cm, the diameter to 0.50 mm, and the tension increased to 100 N, the new frequency can be determined using the equations f1/f2 = L2/L1, f1/f2 = √(F1/F2), and f1/f2 = d2/d1. The final frequency is calculated by combining the effects of these changes on wave speed and wavelength.

PREREQUISITES
  • Understanding of wave mechanics and frequency calculations
  • Familiarity with the relationship between tension, length, and frequency in strings
  • Knowledge of the wave equation v = fλ
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the effects of tension on wave speed in strings
  • Learn how to apply the wave equation v = fλ in practical scenarios
  • Explore the relationship between diameter and frequency in string instruments
  • Investigate how to combine multiple variable changes in frequency calculations
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Students in physics, particularly those studying wave mechanics, as well as educators and anyone interested in the principles of sound production in strings.

justinh8
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Homework Statement


Hi, i need some help with this question,
A string of length 60cm and diameter 0.80 mm is under tension 64 N. When plucked, it emits a frequency of 660Hz. What is the new frequency if the length is decreased to 40cm, the diameter decreased to 0.50mm and the tension increased to 100 N? Please explain, Thanks!


Homework Equations


f1/f2 = L2/L1, f1/f2 = Square Root F1/ Square Root F2, f1/f2 = d2/d1


The Attempt at a Solution


I can do it when one of the variables are decreased but i have no idea where to start when 3 variables are changing.
 
Physics news on Phys.org
The wave speed depends on the tension, the wavelength depends on the length of the string. Do each separately and combine to get frequency. The equation you are missing is v=fλ.
 

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