What are the frequencies of the fundamental and first two overtones?

In summary, the conversation discussed the calculation of frequencies for the fundamental and first two overtones of a guitar string with specific length, mass, and tension. The fundamental tone is heard when the length of the string is equal to half the wavelength, and the distance between two adjacent nodes is equal to half the wavelength. The incorrect calculation of the unit mass may have caused errors in finding the frequencies.
  • #1
jlwood13
5
0

Homework Statement


A guitar string is 90.0 cm long and has a mass of 3.17 g. From the bridge to the support post is 60.0 cm and the string is under a tension of 506 N. What are the frequencies of the fundamental and first two overtones? (f1,f2,f3)


Homework Equations


v=sqrt(FT/m/l)
v=[tex]\lambda*f[/tex]


The Attempt at a Solution


I checked in my text and found that for f1, l=1/2[tex]\lambda[/tex]1; for f2, l=[tex]\lambda[/tex]2; and for f3, l=3/2[tex]\lambda[/tex]3. I tried using 60.0 cm (and converted to meters) and 90.0 cm (converted to meters) and 30.0 cm (converted to meters) for l, but nothing worked. I also converted 3.17 g into kilograms so that's not an issue. I'm not sure what to do now..
 
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  • #2
The fundamental tone is heard when the length of the guitar sting equals half the wavelenght (corresponding to the fundamental tone).

Due to the construction of the guitar, you will get a node in both ends, and the distance between 2 adjacent nodes is lamda/2.

EDIT:

My error, I didn't read the assignment carefully. You have to use 60 cm and not 90 cm.
 
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  • #3
Yeah for the fundamental 60cm is only 1/2 of it. - Wavelegnth for the fundamental = 120cm.

I'm struggling to see what you've done wrong, I think it might just be a case on number crunching wrong. Bear in mind the wavelegnth figure you'd use is 2x 60cm, however the mass per unit legnth you'd use is 90cm... What do you mean "nothing worked" what sort of answers were you getting? Bear in mind that if it's 506N the speed would have to be damn fast :P, I get a very high speed

edit; welcome to pforums ;p
 
  • #4
I am not totally sure on this, but since it states that the whole string has a mass of 3.17 gram, doesn't that mean that the 60 cm has a smaller mass? If the answer is wrong it might be because of the wrong value on mass.

EDIT:

I didn't notice that this was exactly what Chewy said, I am sorry.
 
Last edited:
  • #5
That makes no difference, you're trying to work out the mass per unit legnth, since the whole string weighs 3.17 grams, & the whole string is 60cm long your calculation must be

0.00317 / 0.9 to work out m0, but again, what sort of answers are you churning out?
 
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  • #6
Isn't it 0.00317/0.9 since it says that the whole string has the mass 3.17 grams?
 
  • #7
Yah, that's what i meant sorry :DD
 
  • #8
When dividing my the unit mass I used .6 instead of .9. It was an error in number crunching. Thanks for your help! Sorry that I didn't respond sooner. Also, thanks for the welcome!
 

FAQ: What are the frequencies of the fundamental and first two overtones?

What exactly are the fundamental frequency and overtones?

The fundamental frequency is the lowest frequency at which a physical system can vibrate. It is the primary frequency at which a string, air column, or other medium can resonate. Overtones are higher frequencies that are integer multiples of the fundamental frequency. The first overtone is the second frequency in the harmonic series, followed by the second overtone which is the third frequency, and so on.

How are the frequencies of the fundamental and first two overtones calculated?

The frequency of the fundamental can be calculated using the formula f = 1/T, where T is the period of the vibration or wave. The frequency of the first overtone is twice the frequency of the fundamental, and the frequency of the second overtone is three times the frequency of the fundamental. In general, the frequency of the nth overtone is n times the frequency of the fundamental.

Can the frequencies of the fundamental and overtones change?

Yes, the frequencies of the fundamental and overtones can change depending on the physical characteristics of the system. For example, the length, tension, and density of a string can affect the frequencies of its fundamental and overtones. In addition, external factors such as temperature and pressure can also impact the frequencies of the fundamental and overtones.

How do the frequencies of the fundamental and overtones affect the sound of an instrument?

The frequencies of the fundamental and overtones determine the pitch and timbre of a sound produced by an instrument. The fundamental frequency determines the pitch, while the overtones contribute to the timbre or quality of the sound. Different instruments have different patterns of overtones, which is what gives them their unique sound.

Are the frequencies of the fundamental and overtones the same for all musical instruments?

No, the frequencies of the fundamental and overtones vary depending on the physical properties and design of each instrument. For example, a piano and a guitar playing the same note will produce different frequencies of the fundamental and overtones due to the differences in their construction and materials. This is what gives each instrument its distinct sound.

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