Frequencies of the first three overtones in a string?

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To find the frequencies of the first three overtones for the A and E strings of a violin, the fundamental frequency and tension must be considered. The formula f = v/λ, where v = √(T/P), is essential for calculating the frequencies. For the A string tuned at 440 Hz with a linear density of 1.00 g/m and tension of 25.0 N, the wavelengths and overtones can be derived using the relationship λ = 2L/n. The calculations for the first three overtones involve substituting n values into the frequency formula. The discussion emphasizes solving the problem without a calculator.
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Homework Statement



A violin has an A string in tune at 440.0 Hz; as is the E string at 660.0 Hz. The tension force on each of the strings is 25.0 N. The linear density of the A string is 1.00 g/m. What are the frequency of the first three overtones for each string?

Homework Equations


f = v/ λ
λ = 2L/n
v = √(T/P)

f = frequency
λ = wavelength
v = velocity of wave
L = string length
T = tension
P = Linear Density in kg/m
n = number of loops

The Attempt at a Solution


String A:

f = (n√(T/P))/2L
L = 0.17967748671

f = (2√(T/P))/2L for the 1st overtone
f = (3√(T/P))/2L for the 2nd overtone
f = (4√(T/P))/2L for the 3rd overtone

Is this path right?
 
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Do this without a calculator.
 
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PietKuip said:
Do this without a calculator.

Oh yeah, thanks!
 
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