# Harmonic Frequency of a String

## 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?

Doc Al
Mentor
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
Mentor
Also: Be mindful of the word "NOT" in the question:
which of the following is NOT a possible harmonic frequency for this string?

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
Mentor
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?

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