Chapter 12, Problem 43P

To determine

The beat frequency.

Answer to Problem 43P

  $f=3\text{ Hz}\text{.}$

Explanation of Solution

Given:

Frequency ( f₁ ) = 294 Hz.

Tension decreased by ( T )= 2%

Formula used:

  $\sqrt{\frac{T_2}{T_1}}=\frac{f_2}{f_1}$

Calculation: 

Since the violin strings have the same wavelength,

  $\sqrt{T_1}\times f_1=\sqrt{T_2}\times f_2$

  $\sqrt{\frac{T_2}{T_1}}=\frac{f_2}{f_1}$

  $\frac{f_2}{f_1}=\sqrt{\frac{\left(100-2\right)}{100}}$$\frac{f_2}{f_1}=0.989$

  $f_2=0.989\times f_1$

  $f_2=0.989\times 294\text{ Hz}\text{.}$

  $f_2=291\text{ Hz}\text{.}$

  $\begin{array}{l}f=f_1-f_2=2.95\text{ Hz}\text{.}\\ f=3\text{ Hz}\text{.}\end{array}$

Conclusion: 

The beat frequency that can be heard is 3 Hz.