What is the fundamental frequency of the string?

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.
  • #1
mattmannmf
172
0
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
 
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  • #2
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)
 
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  • #3
.

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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