Can a 60 cm Guitar String Reach Frequencies Up to 20 kHz?

[sowmit]

Homework Statement

A 60 cm guitar string under a tension of 50.000N has a mass per unit length of 0.100 g/cm. What is the highest resonant frequency that can be heard by a person capable of hearing frequencies up to 20000 HZ?

Homework Equations

f= n/2L * sqrt(F/ greek letter mu)

wavelength = velocity/ frequency. ($$\lambda$$= v*f)

The Attempt at a Solution

I have mu = .100g/cm = .01 kg/m
f= 20000 HZ (not sure if this applies)
L= 60 cm = .6m

When I use,
f= n/2L * sqrt(F/ greek letter mu), I don't have n and I don't know how to find it.


Soneone please help. It's part of my final and worth 15 points. That's a letter grade. The answer is 19 khz or .019 hz.

 

[Matterwave]

n is the highest integer that would not make f>20,000

 

[sowmit]

But I am not sure how to find it. Anyhelp?

 

[ojs]

isolate the frequency equation you have for n, find what n you get by setting 20.000 Hz for f, then take the floor of that n (so if you get 2.92344 use n = 2).

 

[sir_manning]

n must be an integer, so if you are given a frequency your equations allow you to check if it is a resonance frequency. Is 20,000 Hz a resonance frequency? What does this tell you about n?

 

[berkeman]

Homework Statement

A 60 cm guitar string under a tension of 50.000N has a mass per unit length of 0.100 g/cm. What is the highest resonant frequency that can be heard by a person capable of hearing frequencies up to 20000 HZ?

Homework Equations

f= n/2L * sqrt(F/ greek letter mu)

wavelength = velocity/ frequency. ($$\lambda$$= v*f)

The Attempt at a Solution

I have mu = .100g/cm = .01 kg/m
f= 20000 HZ (not sure if this applies)
L= 60 cm = .6m

When I use,
f= n/2L * sqrt(F/ greek letter mu), I don't have n and I don't know how to find it.


Soneone please help. It's part of my final and worth 15 points. That's a letter grade. The answer is 19 khz or .019 hz.

You are asking for our help on your take-home final exam? Could you please PM me the contact information for your professor, so that I can check that s/he is okay with this?

 

[sowmit]

Well it's not final exam. It's final homework problem set which is worth 15% of our grades. And this problem set is consisted of 4 homework problems and if I get one wrong, the whole 15% is gone. And you don't even have to ask him. All the students are allowed to get all the help they can in order to finish these problems. He even suggested us some solution book that I didn't buy just for doing 4 physics problems.

 

[berkeman]

Well it's not final exam. It's final homework problem set which is worth 15% of our grades. And this problem set is consisted of 4 homework problems and if I get one wrong, the whole 15% is gone. And you don't even have to ask him. All the students are allowed to get all the help they can in order to finish these problems. He even suggested us some solution book that I didn't buy just for doing 4 physics problems.

So far in this thread, I've seen zero effort by you to solve the question. You are just trolling for help. Post your attempt at a solution, and make it good. We do not do you schoolwork for you here.