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 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.

Answer 1

Answer:

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

$f=$ Frequency of Kira

$f_1=$ Frequency of Aiko

The beat frequency of Kira and Aiko is therefore,

$f_{beat}=|f_2-f_1|$

Substituting  $f$  for  $f_2$  and $3Hz$ for $f_{beat}$ , we get

$3Hz=|f-f_1|\\f_1=f+3Hz$

From the above equation, we see that beats increase

when

$f_2 =$ Frequency of Chandra

The beat frequency of Kira and Chandra is therefore,

$1Hz=|f-f_2|\\f_2=f-1Hz$

From the above equation, we see that beats decrease

When

$f_3=$ Frequency of Evita

The beat frequency of Kira and Evita is therefore,

$5Hz=|f-f_3|\\f_3=f-5Hz$

From the above equation, we see that beats decrease

When

$f_4=$ Frequency of Freja

The beat frequency of Kira and Freja is therefore,

$3Hz=|f-f_4|\\f_4=f-3Hz$

From the equation above, we see that beats decrease

When

$f_5=$ Frequency of Buffy

The beat frequency of Kira and Buffy becomes,

$4Hz=|f-f_5|\\f_5=f+4Hz$

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