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An all female guitar septet is getting ready to go on stage. The lead guitarist, Kira, who is...

Question:

An all female guitar septet is getting ready to go on stage. The lead guitarist, Kira, who is always in tune, plucks her low E string and the other six members, sequentially, do the same. Each member records the initial beat frequency {eq}f_{beat,i} {/eq} between her low E string and Kira's low E string.

Rank each member on the basis of the initial frequency of their low E string.

rank from largest to smallest :

Diane : f{eq}_{beat,i} {/eq} = 0 Hz

Freja : f{eq}_{beat,i} {/eq} = 3 Hz

Aiko: f{eq}_{beat,i} {/eq} = 3 Hz

Chandra: f{eq}_{beat,i} {/eq} = 1 Hz

Evita: f{eq}_{beat,i} {/eq} = 5 Hz

Buffy : f{eq}_{beat,i} {/eq} = 4 Hz

Beat Frequency

Beat frequency is an outcome of interference in sound. When two near by frequencies of sound interfere the listeners will hear alternate sound maxima and minima. The minima will be very small so may nor hear but what the listener will hear is the maxima alone. One maxima and minima makes one beat. The number of beats can be counted by just counting the maxima alone. The beat frequency will be equal to the difference frequency between the two sounds. Beat frequency {eq}F_b = | F_1 - F_2 | {/eq}. Here {eq}F_1, \ \ F_2 {/eq} are the frequencies played together.

Answer and Explanation:

Given points

  • Low E sting Frequency played by Kira F
  • Beat frequency of the members {eq}F_{bD} = 0 \\ F_{bF} = 3 \ Hz \\ F_{bA } = 3 \ Hz \\ F_{bC} = 1 \ Hz \\ F_{bE} = 5 \ Hz \\ F_{bB } = 4 \ Hz {/eq}
  • Let {eq}F_1, \ \ F_2, \ \ F-3, \ \ F_4 , \ \ F_5, \ \ F_6 {/eq} be the low E string frequencies played by Diane, Freja, Aiko, Chandra, Evita, and Buffy respectively

For any member beat frequency is the difference frequency between the Kira's low E string frequency. So the frequency played by the member can be either lower than or greater than the standard frequency. We can only say the members frequency is how different from the standard frequency.

So we rank the members based on the largest difference to smallest difference in frequency to the standard frequency we get the following order

{eq}Evita \ \ > \ \ Buffy \ \ > \ \ Freja \ \ = \ \ Aiko > \ \ Chandra \ \ > \ \ Diane {/eq}


Learn more about this topic:

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Interference Patterns of Sound Waves

from MTEL Physics (11): Practice & Study Guide

Chapter 16 / Lesson 5
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