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 between her low E string and Kira's low E string.

To tune an instrument using beats, more information than just the beat frequency is needed. In addition to recording the initial beat frequency , each member, except Diane, also records the change in the frequency (increase or decrease) when they increase the tension in their low E string.

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

Rank from largest to smallest. To rank items as equivalent, overlap them.

Aiko=3Hz, fbeat increases

Chandra=1Hz fbeat decreases

Evita=5Hz fbeat decreases.

Freja=3Hz fbeat decreases.

Buffy=4Hz fbeat increases.

Buffy > Aiko > Chandra > Freja > Evita

Explanation:

Beats occur when two waves of nearby frequencies overlap. The number of beats per second is equal to the difference in the frequency.

Let

Frequency of Kira

Frequency of Aiko

The beat frequency of Kira and Aiko is therefore,

Substituting    for    and for , we get

From the above equation, we see that beats increase

when

Frequency of Chandra

The beat frequency of Kira and Chandra is therefore,

From the above equation, we see that beats decrease

When

Frequency of Evita

The beat frequency of Kira and Evita is therefore,

From the above equation, we see that beats decrease

When

Frequency of Freja

The beat frequency of Kira and Freja is therefore,

From the equation above, we see that beats decrease

When

Frequency of Buffy

The beat frequency of Kira and Buffy becomes,

From the equation above, we see that beats increase

Hence, the rank of members based on initial frequencies from largest to smallest is Buffy > Aiko > Chandra > Freja > Evita

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