Since the tuba creates a 4th harmonic of frequency 116.5 hz, the length of pipe in tuba is 6.57 m
Since the tuba is an closed-pipe instrument, we need to find the frequency of a closed pipe
The frequency of a closed pipe f = nV/4L where
Making L subject of the formula, we have
L = nV/4f
Since the tuba creates the 4th harmonic with frequency 116.5 Hz.
Substituting the values of the variables into the equation, we have
L = nV/4f
L = 9 × 340 m/s/4 × 116.5 Hz
L = 3060 m/s ÷ 466 Hz
L = 6.57 m
So, the length of pipe in tuba is 6.57 m
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