# Harmonic Frequency of a String

• Aiyan
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.

## 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

• 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?

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!

• Delta2