Chapter 11, Problem 53P

To determine

To Find: The fingered frequency required to vibrates the string of violin.

Answer to Problem 53P

The fingered frequency at which the violin string vibrates is $441\text{ Hz}$ .

Explanation of Solution

Given:

Unfingered frequency $f=294\text{ Hz}$

Fingered length $l=\frac{2}{3}\times l$

Formula used:

The expression for fundamental frequency of full shift.

  $f=\frac{v}{2\times l}$ .

Here,

  $f$ is the string frequency,

  $v$ is speed of sound,

  $l$ is the length of vibrating string.

Calculation:

Substitute the given values in the above equation,

  $\begin{array}{l}\text{Fingered frequency }f=\frac{v}{2\times \left(\frac{2}{3}\times l\right)}=\frac{3}{2}\times \frac{v}{2\times l}\\ \text{Fingered}\text{}\text{ frequency }f=\frac{3}{2}\times 294=441\text{ Hz}\end{array}$

Conclusion:

Thus, the fingered frequency at which the violin string vibrates is $441\text{ Hz}$ .