# What is the fundamental frequency of the string?

• mattmannmf
In summary, the harmonics on a string 1.4 meters long have frequencies of 18.4 Hz and 23.9 Hz. To find the fundamental frequency, we use the equation f1 = v/2L, which gives us a value of 5.5 Hz. To find the speed of the waves on the string, we can use the equation v=hf, where h is the difference in frequencies between successive harmonics and f is the fundamental frequency. We can also use the equation ω = nπv/L, and convert the angular frequency to Hertz.
mattmannmf
One of the harmonics on a string 1.4 meters long has a frequency of 18.4 Hz. The next higher harmonic frequency is 23.9 Hz.

(a) What is the fundamental frequency of the string?
f1 = Hz *
5.5 OK

(b) What is the speed of the waves on the string?
v = m/sec

the URL:https://wug-s.physics.uiuc.edu/cgi/cc/shell/DuPage/Phys1201/spring/tma.pl?Ch-14-Waves/wt_fundamental#pr

I found the frequency, but I am just a little confused on how to find the speed. i know i have to use the equation: v=hf. but I am just confused on how to find wavelength... wavelength is the distance it takes to complete a full cycle correct? i don't know where I am going wrong in my calculations

Last edited by a moderator:
You know the difference between the frequencies of successive harmonics is 5.5 Hz. This difference is a function of v and L, and you already know L.

(Hint: Use ω = nπv/L, you have to convert the angular frequency here to Hertz)

Last edited:
.

To find the speed of the waves on the string, we can use the equation v=λf, where v is the speed, λ is the wavelength, and f is the frequency. We already have the frequency (f) from the given information. To find the wavelength, we can use the formula λ=2L/n, where L is the length of the string and n is the harmonic number (in this case, n=1 for the fundamental frequency).

Substituting the values, we get:

λ=2(1.4m)/1 = 2.8m

Now, we can plug in the values of f and λ in the equation v=λf to find the speed:

v=(2.8m)(18.4Hz) = 51.52 m/s

Therefore, the speed of the waves on the string is 51.52 m/s.

Note: In this case, we are assuming that the string is under tension and has a linear mass density (mass per unit length) given. If these values are not provided, we cannot accurately calculate the speed of the waves.

## What is the fundamental frequency of the string?

The fundamental frequency of a string is the lowest frequency at which it will naturally vibrate when plucked, struck, or bowed.

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

The fundamental frequency of a string is determined by its length, tension, and density. This can be calculated using the formula 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 density.

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

The fundamental frequency of a string can be affected by its length, tension, and density, as well as any external forces such as air resistance or friction.

## Can the fundamental frequency of a string be changed?

Yes, the fundamental frequency of a string can be changed by adjusting its length, tension, or density. This can be done by changing the position of frets on a guitar or adjusting the tuning pegs to tighten or loosen the string.

## Why is the fundamental frequency important in music?

The fundamental frequency is important in music because it determines the pitch of a note produced by a string instrument. It also plays a role in creating overtones and harmonics, which contribute to the overall sound and timbre of the instrument.

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