Musical wind instruments change notes by changing the length of a tube which is

Question

Musical wind instruments change notes by changing the length of a tube which is open on both ends. However many times the same note can be played on different lengths of tube. A note of “C” with a frequency of  260 Hz can be played on a tube with a length of 1.32 m. ( speed of sound 343 m/s)

a. Is this the fundamental frequency of the tube ?

b. Which harmonic is being observed ?

c. What length of tube would have a fundamental frequency of 260 Hz ?

d. What is the next longest piece of tube that will produce a frequency of 260 Hz ?

e. Calculate the wavelength for parts “c” and “d

Explanation / Answer

a)
fundamental frequency,
f1 = v/2L
= 343/(2*1.32)
=130 hz
so, 260 Hz is not the fundamental frequency
Answer: No

b)
fn = nv/2L
260= n*130
n=2
This is harmonic number 2

c)
f1 = v/2L
260 = 343/(2*L)
L=0.66 m
Answer: 0.66 m

d)
0.66 m will provide that

e)
wavelength = speed/f
=343/260
       =1.32 m

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