Harmonic Frequency of a String

In summary, the problem involves a vibrating string with a mass of 1 kg and length of 2 m, feeling 50 N of tension. The question asks for the NOT possible harmonic frequency, and through calculations using the given equations, it is determined that the fundamental frequency is 2.5 Hz and therefore, option a) 1.25 Hz is not a possible harmonic frequency. The information about the string vibrating in its second harmonic mode is a red herring and does not affect the possible harmonic frequencies.
  • #1
Aiyan
3
1

Homework Statement


A string (m = 1 kg) fixed at both ends is vibrating in its second harmonic mode. If the length of the string is 2 m and it feels 50 N of tension, which of the following is NOT a possible harmonic frequency for this string?
  • a) 1.25 Hz
  • b) 2.5 Hz
  • c) 5 Hz
  • d) 10 Hz
  • e) 20 Hz

Homework Equations


  • v=sqrt(T/μ)
  • fn=(nv)/(2L)

The Attempt at a Solution


  • μ=1 kg/2 m = 0.5 kg/m
  • The velocity is 10 m/s, from sqrt(50 N/0.5 kg/m)
  • The frequency is 5 Hz, from (2 * 10 m/s)/(2 * 2 m)
4. My thoughts
I feel like this problem has an error, since I actually got a specific answer, and only one answer is possible given all the information from the question. Can someone here please confirm this?
 
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  • #2
Aiyan said:
I feel like this problem has an error, since I actually got a specific answer, and only one answer is possible given all the information from the question. Can someone here please confirm this?
The problem seems OK to me. Hint: What is the fundamental frequency of the string? (The fact that it happens to be vibrating in the second harmonic is a red herring.)
 
  • #3
Also: Be mindful of the word "NOT" in the question:
Aiyan said:
which of the following is NOT a possible harmonic frequency for this string?
 
  • #4
Doc Al said:
The problem seems OK to me. Hint: What is the fundamental frequency of the string? (The fact that it happens to be vibrating in the second harmonic is a red herring.)
f1=v/(2L)=2.5 Hz.
I don't get how the second harmonic information is unrelated, it means that n=2 right?
 
  • #5
Aiyan said:
f1=v/(2L)=2.5 Hz.
Good.

Aiyan said:
I don't get how the second harmonic information is unrelated, it means that n=2 right?
Sure. What about the other modes? Of the frequencies listed, which one is NOT a possible harmonic?
 
  • #6
Doc Al said:
Good.Sure. What about the other modes? Of the frequencies listed, which one is NOT a possible harmonic?
Oh, a) 1.25 Hz because the minimum frequency is 2.5 Hz. Thanks for your help!
 
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1. What is the harmonic frequency of a string?

The harmonic frequency of a string is the fundamental frequency at which the string vibrates when it is plucked or struck. It is the lowest frequency that results in a standing wave pattern on the string.

2. How is the harmonic frequency of a string calculated?

The harmonic frequency of a string can be calculated using the equation f = (1/2L) * √(T/μ), where f is the frequency, L is the length of the string, T is the tension in the string, and μ is the mass per unit length of the string.

3. Can the harmonic frequency of a string be changed?

Yes, the harmonic frequency of a string can be changed by altering the length, tension, or mass of the string. Shortening the string or increasing the tension will result in a higher harmonic frequency, while lengthening the string or decreasing the tension will result in a lower harmonic frequency.

4. How does the harmonic frequency of a string affect the sound it produces?

The harmonic frequency of a string determines the pitch of the sound it produces. A higher harmonic frequency will result in a higher pitch, while a lower harmonic frequency will result in a lower pitch.

5. Are there multiple harmonic frequencies for a single string?

Yes, there are multiple harmonic frequencies for a single string. These are known as overtones or harmonics, and they are whole number multiples of the fundamental frequency. The second harmonic, for example, is twice the frequency of the fundamental, and the third harmonic is three times the frequency of the fundamental.

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