Question

If a wind instrument, such as a tuba, has a fundamental frequency of 56.0 Hz, what are its first three overtones (in Hz)? It is closed at one end. (The overtones of a real tuba are more complex than this example, because it is a tapered tube.)

Answer 1

Answer:

168 Hz, 280 Hz and 392 Hz

Explanation:

The resonant frequencies for a closed pipe at one end is given by :

$f=\dfrac{nv}{4L}$, n = 1,3,5...

The fundamental frequency, f₁ = v/4l = 56 Hz

For first overtone, put n = 3

$f_3=\dfrac{3v}{4L}\\\\=3\times \dfrac{v}{4L}\\\\=3\times 56\\\\=168\ Hz$

For second overtone, put n = 5

$f_5=5\times f_1\\\\=5\times 56\\\\=280\ Hz$

For third overtone, put n = 7

$f_7=7\times f_1\\\\=7\times 56\\\\=392\ Hz$

So, the first three overtones are 168 Hz, 280 Hz and 392 Hz.