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A piano tuner detects 3 beats per second when she is tuning a string to a tuning fork of frequency 440 Hz. When she tightens the string, which increases the frequency of the string, the frequency of the beats initially goes down, and as she keeps increasing the frequency of the string, the frequency of the beats starts to increase. What was the original frequency of the string

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okpalawalter8

Answer:

[tex]F_o=437Hz[/tex]

Explanation:

From the question we are told that:

Frequency of Turning fork [tex]F_t=440Hz[/tex]

Number of beats detected [tex]n=3[/tex]  

Generally the equation for Original frequency [tex]F_o[/tex] of the string  is mathematically given by

[tex]F_o=F_t-F_b[/tex]

Where

[tex]F_b[/tex] Beat frequency

[tex]F_b=1Hz*n\\F_b=1Hz*3[/tex]

Therefore

[tex]F_o=440-3[/tex]

[tex]F_o=437Hz[/tex]

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