Answer:
93.54 Hz
Step-by-step explanation:
✓From the question, Number of harmonic frequency is 4
✓ the frequency (f₄ )= 116.5 Hz
✓harmonic frequency can be calculated using below expresion
fₙ = [ (nv)/4L]..........eqn(1)
v = speed of sound= 343 m/s
n = number of given harmonic frequency
L = Length of the rope
Using above expresion ,and substitute the values at (n=4) which is 4th harmonic frequency to find the " initial Lenght of the rope
fₙ = [ (nv)/4L]
f₄ = 4× 343 /4L
f₄ = 343 /L
L= 343 /f₄
But f₄= 116.5 Hz
L= 343/116.5= 2.944m
Hence, initial Lenght of the rope= 2.944m
We can determine the frequency of new length as ( initial Lenght of the rope + tubing Lenght)
= ( 2.944m + 0.721m )
= 3.667m
Hence, new length= 3.667m
To find the new frequency of the 4th harmonic we will use eqn(2)
f₄ = v/l ...............eqn(2)
From equation (2) If we substitute the values we have
f₄ = (343/3.667)
= 93.54 Hz
Hence, the the new frequency of the 4th harmonic is
93.54 Hz