The notes produced by a tuba range in frequency from approximately 45 Hz to 375 Hz. Find the possible range of wavelengths in air produced by the instrument when the speed of sound in air is 343 m/s.
The relationship for wavespeed and the properties of a wave are given by the relationships
S = df where S is speed, d is the distance traveled, and f is frequency
S = d/T where T is the period
S = Wf where W is the wavelength
and S = W/T
For this given problem we can find the minimum and maximum wavelengths rearranging the S = Wf equation.
W = S/f
for the lowest note of 45 Hz (45/second) we get W = (343m/s)/(45/s) = 7.62 m
for the highest note of 375Hz (375/seconds) we get
W=(343m/s)/(375/s) = 0.915 m.
Therefore the range of wavelengths is between 0.915m to 7.62m.