Question

Guitar string has an overall length of 1.22 m and a total mass of 3.5 g before being strung on a guitar. Once it is used on the guitar, there is a distance of 70 cm between fixed end points. The guitar string is tightened to a tension of 255 N.
What is the frequency of the fundamental wave on the guitar string?

Answer 1

Answer:

Fundamental frequency= 174.5 hz

Explanation:

We know

fundamental frequency=$\frac{velocity}{2 *length}$

velocity =$\sqrt{\frac{tension}{mass per unit length} }$

mass per unit length=$\frac{3.5}{1000*1.22}$=0.00427$\frac{kg}{m}$

Now calculating velocity v=$\sqrt{\frac{255}{0.00427} }$

                                           =244.3$\frac{m}{sec}$

Distance between two nodes is 0.7 m.

Plugging these values into to calculate frequency

f = $\frac{244.3}{2 *0.7}$ =174.5 hz