Chapter 26, Problem 23A

A pair of tuning forks of frequencies $f_1$ and $f_2$ are sounded together.

Rank from greatest to least the beat frequencies produced by the following pairs of tuning forks.

(A) $f_1=650\text{Hz};f_2=654\text{Hz}$

(B) $f_1=300\text{Hz};f_2=305\text{Hz}$

(C) $f_1=200\text{Hz};f_2=208\text{Hz}$

(D) $f_1=800\text{Hz};f_2=801\text{Hz}$

To determine

To rank the beat frequency of the given pairs of frequencies.

Answer to Problem 23A

1: (C) f₁= 200 Hz, f₂= 208 Hz

2: (B) f₁= 300 Hz, f₂= 305 Hz

3: (A) f₁= 650 Hz, f₂= 654 Hz

4: (D) f₁=800 Hz, f₂=801 Hz

Explanation of Solution

Given info:

The frequency pairs are

  

Formula used:

The beat frequency is

  ${\text{f}}_{\text{beat}}\text{=}\left|{\text{f}}_{\text{1}}{\text{-f}}_{\text{2}}\right|$$$

Calculation:

Substituting the given values, we get

  $\begin{array}{l}\left(\text{A}\right){\text{ f}}_{\text{beat}}\text{=}\left|\text{650 HZ-654 Hz}\right|\\ {\text{ f}}_{\text{beat}}\text{=4 Hz}\\ \left(\text{B}\right){\text{ f}}_{\text{beat}}\text{=}\left|\text{300 HZ-305 Hz}\right|\\ {\text{ f}}_{\text{beat}}\text{=5 Hz}\\ \left(\text{C}\right){\text{ f}}_{\text{beat}}\text{=}\left|\text{200 HZ-208 Hz}\right|\\ {\text{ f}}_{\text{beat}}\text{=8 Hz}\\ \left(\text{D}\right){\text{ f}}_{\text{beat}}\text{=}\left|\text{800 HZ-801 Hz}\right|\\ {\text{ f}}_{\text{beat}}\text{=1 Hz}\end{array}$

Conclusion:

Thus, the rank of the beat frequency from greatest to least is

1: (C) f₁= 200 Hz, f₂= 208 Hz

2: (B) f₁= 300 Hz, f₂= 305 Hz

3: (A) f₁= 650 Hz, f₂= 654 Hz

4: (D) f₁=800 Hz, f₂=801 Hz