Frequencies of the first three overtones in a string?

In summary, the conversation discusses the frequency of the first three overtones for the A and E strings of a violin, which are in tune at 440.0 Hz and 660.0 Hz respectively. The tension force on each string is 25.0 N, and the linear density of the A string is 1.00 g/m. The equations used to solve for the frequency of the overtones involve the velocity of the wave, string length, tension, and linear density. The attempt at a solution suggests using the equation f = (n√(T/P))/2L and provides values for the first three overtones. The conversation also mentions attempting to solve this without a calculator.
  • #1
Tom Beckham
2
1

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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  • #2
Do this without a calculator.
 
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  • #3
PietKuip said:
Do this without a calculator.

Oh yeah, thanks!
 
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1. What are overtones in a string?

Overtones are additional vibrations that occur in a string due to its shape and material. They are multiples of the fundamental frequency and can be heard as higher pitches.

2. How do overtones affect the sound of a string?

Overtones contribute to the timbre or tone quality of a string's sound. They give the sound its unique characteristics and can make it sound richer or more complex.

3. What are the first three overtones in a string?

The first three overtones in a string are the second, third, and fourth harmonic frequencies. These correspond to twice, three times, and four times the fundamental frequency, respectively.

4. How do you calculate the frequencies of the first three overtones in a string?

The frequencies of the first three overtones can be calculated by multiplying the fundamental frequency by 2, 3, and 4, respectively. For example, if the fundamental frequency is 100 Hz, the first overtone would be 200 Hz, the second overtone would be 300 Hz, and the third overtone would be 400 Hz.

5. What factors affect the frequencies of overtones in a string?

The frequencies of overtones in a string can be affected by factors such as the tension, length, and thickness of the string, as well as the material it is made of. These factors can alter the shape and size of the string, which in turn affects the wavelengths of the overtones.

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