Harmonic Frequency of a String

[Aiyan]

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)
• f_n=(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?

 

[Doc Al]

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.)

 

[Doc Al]

Also: Be mindful of the word "NOT" in the question:

which of the following is NOT a possible harmonic frequency for this string?

 

[Aiyan]

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?

 

[Doc Al]

f1=v/(2L)=2.5 Hz.

Good.

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?

 

[Aiyan]

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!