# Fundamental Frequency of a string

• nn3568
In summary, the string has a length of 1440 cm and is held fixed at each end. It vibrates in eight sections, with eight antinodes and a fundamental frequency of 150 Hz. Using the formula f = nv/2L, with n representing the number of antinodes, we can calculate the velocity of the string to be 540 m/s. However, when trying to find the first harmonic or fundamental frequency, there was confusion as to whether to use the velocity or not. It was eventually determined that the fundamental frequency is 1/8 of the total frequency and is used with 2*L in the formula to find the velocity.
nn3568

## Homework Statement

The length of a string is 1440 cm. The
string is held fixed at each end. The string
vibrates in eight sections; i.e., the string has
eight antinodes, and the string vibrates at
150 Hz.

What is the fundamental frequency? Answer
in units of Hz.

## Homework Equations

f = nv / 2L frequency = (# antinodes)(velocity) / (2 * length)

## The Attempt at a Solution

I already found the wavelength which is 3.6 m. I got that by substituting nv/2L for f into the equation v=λf (velocity = wavelength*frequency). Then I followed the above frequency formula:

v=λf
v=(3.6 m)(150 Hz) = 540 m/s

f = nv / 2L
f = (8)(540 m/s) / (2*14.4 m) = 150 Hz

My online HW said it was wrong. So I tried again.

f = (2)(540 m/s) / (2*14.4 m) = 37.5 Hz

I used two because it said that fundamental frequency is the lowest frequency and you can use the first harmonic or something. Didn't really understand it. But the two is because the 1st harmonic has 2 antinodes.

I am so confused and I have no clue what I am doing! Please help <:S

Last edited:
If there are 8 antinodes then there are 4 wavelengths represented on the string.

But I think 8 antinodes means it's the 8'th harmonic of the string.

So isn't 1/8 of 150 hz then the first harmonic and isn't that the frequency you use with 2*L to determine v?

Or do you not need to find the v?

Only the f1 fundamental frequency?

i already found v. i just don't understand the fundamental frequency part.

nn3568 said:
i already found v. i just don't understand the fundamental frequency part.

8 antinodes means 8th harmonic = 8 times the fundamental frequency (first harmonic).

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/sound/u11l4d.html

Last edited by a moderator:

## What is the fundamental frequency of a string?

The fundamental frequency of a string is the lowest frequency at which the string can vibrate. It is also known as the first harmonic and is determined by the length, tension, and mass of the string.

## How is the fundamental frequency of a string calculated?

The fundamental 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, and μ is the linear mass density of the string.

## What factors affect the fundamental frequency of a string?

The fundamental frequency of a string is affected by the length, tension, and mass of the string. It also depends on the material, thickness, and stiffness of the string.

## What is the relationship between the fundamental frequency and the harmonics of a string?

The fundamental frequency is the first harmonic of a string, and the higher harmonics are integer multiples of the fundamental frequency. This means that the second harmonic is twice the frequency of the fundamental, the third harmonic is three times the frequency, and so on.

## How does the fundamental frequency of a string relate to musical pitch?

The fundamental frequency of a string determines the pitch of the sound produced by the string. As the fundamental frequency increases, the pitch also increases. This is why longer strings produce lower pitches and shorter strings produce higher pitches.

Replies
5
Views
1K
Replies
5
Views
2K
Replies
2
Views
1K
Replies
5
Views
6K
Replies
2
Views
3K
Replies
1
Views
2K
Replies
2
Views
1K
Replies
3
Views
2K
Replies
7
Views
2K
Replies
14
Views
1K