Answer:
The new frequency is:
f₄ = 93.54 Hz
Step-by-step explanation:
The data given to us is:
No. of harmonic frequency = 4
f₄ = 116.5 Hz
We know that the harmonic frequency is given by the formula:
fₙ = (n · v)/4L
where
n = no. of harmonic frequency
v = speed of sound
L = Length of rope
Lets find the initial length of rope for 4rth harmonic frequency (n=4) and v=343 m/s
fₙ = (n · v)/4L
f₄ = 4v/4L
f₄ = v/L
L = v/f₄
L = 343/116.5
L= 2.944m
Find frequency for new length that is 2.944m + 0.721m = 3.667m
f₄ = v/l
f₄ = 343/3.667
f₄ = 93.54 Hz