A tuba may be treated like a tube closed at one end. If a tuba has a fundamental frequency of 40.4 Hz, determine the first three overtones. Use 343 m/s as the speed of sound in air. If the speed of sound is 337 m/s, determine the length of an open tube (open at both ends) that has a fundamental frequency of 233 Hz and a first overtone frequency of 466 Hz.

Explanation:

fundamental frequency at closed pipe = 40.4 Hz

overtones are odd harmonics in closed pipe

first three overtones are

3 x 40.4 , 5 x 40.4 , 7 x 40.4 Hz

= 121.2 Hz , 202 Hz , 282.8 Hz .

speed of sound given is 337 , fundamental frequency is 233 Hz

wavelength = velocity of sound / frequency

= 337 / 233

= 1.446 m

for fundamental note in open pipe

wavelength /2 = length of tube

length of tube = 1.446 / 2

= .723 m

= 72.30 cm .

first overtone will be two times the fundamental ie 466. In open pipe all the harmonics are found , ie both odd and even .

massxgravity x heght=weightxheight= pe

4900=490xh

h=10