Question

A uniform string of length 2.5 m and mass 0.01 kg is placed under a tension of 10 N. (5 pts) A) What is the frequency of the fundamental mode

Answer 1

The fundamental frequency is 10 Hz

Step-by-step explanation:

The frequency of the fundamental mode of the string is given by;

`f_o =(1)/(2l)\sqrt{(T)/(\mu )`

where;

L is length of the string = 2.5 m

T is tension of the string, = 10 N

μ is mass per unit length = m / L = 0.01 / 2.5 = 0.004 kg/m

Substitute the given values and solve for the frequency;

`f_o =(1)/(2l)\sqrt{(T)/(\mu )}\\\\ f_o =(1)/(2*2.5)\sqrt{(10)/(0.004)}\\\\ f_o = 0.2√(2500)\\\\ f_o = 0.2 *50\\\\f_o = 10 \ Hz`

Therefore, the fundamental frequency is 10 Hz