Find New Frequency When Length AND Diameter Is Decreased?

AI Thread Summary
To find the new frequency of a string when its length, diameter, and tension change, the relationships between these variables must be considered. The original string has a frequency of 660 Hz, a length of 60 cm, a diameter of 0.80 mm, and a tension of 64 N. When the length is decreased to 40 cm, the diameter to 0.50 mm, and the tension increased to 100 N, the frequency can be calculated using the equations that relate frequency to length, tension, and diameter. The wave speed is influenced by tension, while the wavelength is affected by the string's length. By applying the relevant equations, the new frequency can be determined accurately.
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.
 
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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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