The frequency of the 4th harmonic of a tube closed on one end (like a tuba) is given by the formula:
f = (2n-1)c/4L
Where:
f is the frequency of the nth harmonic
c is the speed of sound
L is the length of the tube
In this case, we are given the frequency of the 4th harmonic as 116.5 Hz and the speed of sound as 343 m/s. We can solve for the fundamental frequency (1st harmonic) by rearranging the formula:
f1 = (2(1)-1)c/4L = c/4L
We need to find the length of the tube to calculate the fundamental frequency. However, we don't have enough information about the length of the tuba. Therefore, we cannot determine the fundamental frequency with the given information.
If we assume that the tuba is a standard B-flat tuba, we can estimate its length to be around 18 feet (5.5 meters). Using this length in the formula, we get:
f1 = c/4L = 343/(4*5.5) = 15.6 Hz
Therefore, if the tuba is a B-flat tuba, the fundamental frequency would be around 15.6 Hz. However, this is just an estimate and the actual length of the tuba could be different, which would affect the fundamental frequency.