Physics Question

Question

Find the fundamental frequency and two other frequencies that will be naturally produced, by a string of mass 5.00g that is 0.750 m long and put under a tension of 360.0 N.

Answer 1

Hi Grace!

 

The formula for harmonic frequencies of a string (fixed at both ends) is:

 

f_n = nv/2L

 

where

 

L = length of the string

v = speed of waves on the string

 

and n is an index variable that can be any non-zero positive integer (1,2,3...).  When n = 1, that is called the fundamental frequency or fundamental harmonic, and all other harmonics (aka overtones) are integer multiples of the fundamental (since f₁ = v/2L, and f_n = n(v/2L) = nf₁).

 

We have the length of the string, but we need to know the speed of waves on the string.  Assuming the string has a uniform (constant) mass density, the speed of waves on the string is given by:

 

v_s = √(T/(m/L)) = √(TL/m)

 

where T = tension on the string and m = mass of the string

 

So, you can solve for v_s with the information given (remember to convert the mass to kg, so it plays nicely with the other values, and gives you v_s in meters per second.

 

Once you solve for v, you can calculate the fundamental frequency (f₁), and then get two other frequencies just by multiplying f₁ by other values of n.

 

I hope that gets you on your way!  Let me know if you have more questions or would like to check an answer.