Aguitar string has a linear density of 8.30 ✕ 10−4 kg/m and a length of 0.660 m. the tension in the string is 56.7 n. when the fundamental frequency of the string is sounded with a 196.0-hz tuning fork, what beat frequency is heard?

Ans: Beat Frequency = 1.97Hz

Explanation:
The fundamental frequency on a vibrating string is 

  -- (A)

here, T=Tension in the string=56.7N,
L=Length of the string=0.66m,
m= mass = 8.3x10^-4kg/m * 0.66m = 5.48x10^-4kg 

Plug in the values in Equation (A)

so  = 197.97Hz 

the beat frequency is the difference between these two frequencies, therefore:
Beat frequency = 197.97 - 196.0 = 1.97Hz
-i

First of all, we need to find the fundamental frequency of the string.

The fundamental frequency of a string is given by:

where L is the length of the string, T the tension and the linear density.
Using the information given in the exercise: L=0.660 m, T=56.7 N and , we find


The beat frequency is given by the difference in frequency between the fundamental frequency of the string and the tuning fork (196 Hz), so it is:

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.