In certain ranges of a piano keyboard more than one string i

In certain ranges of a piano keyboard, more than one string is tuned to the same note to provide extra loudness. For example, the note at 110 Hz has two strings at this frequency. If one string slips from its normal tension of 600 N to 540 N, what beat frequency is heard when the hammer strikes the two strings simultaneously?

Answer is 5.64 HZ

Please show work and explain, thanks!

Solution

Here ,

T1 = 600 N

f1 = 110 Hz

T2 = 540 N

Now , for the frequency f2

f1/f2 = sqrt(T1/T2)

110/f2 = sqrt(600/540)

f2 = 104.36 Hz

Now ,

beat frequency = |f2 - f1|

beat frequency = |110 - 104.36|

beat frequency = 5.64 Hz

the beat frequency produced is 5.64 Hz