Which Frequency is NOT Possible for a Vibrating String?

AI Thread Summary
The discussion revolves around determining which frequency is not possible for a vibrating string fixed at both ends, specifically in its second harmonic mode. The string has a length of 2 m and experiences a tension of 50 N, leading to a calculated velocity of 10 m/s and a fundamental frequency of 2.5 Hz. Participants clarify that the second harmonic information is relevant, but the focus should be on identifying frequencies that can occur. Ultimately, it is concluded that 1.25 Hz is not a possible harmonic frequency for this string, as it is below the minimum frequency of 2.5 Hz. The problem is confirmed to be correctly framed despite initial confusion.
Aiyan
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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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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.)
 
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?
 
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?
 
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?
 
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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