An open organ pipe has a length of 5 cm . Identify the highest...

The fundamental frequency of an open organ pipe is given by $f_1 = \dfrac{v}{2L}$

Substituting $v = 340 \text{ m s}^{-1}$ and $L = 5 \text{ cm} = 0.05 \text{ m}$:

$f_1 = \dfrac{340}{2 \times 0.05} = \dfrac{340}{0.1} = 3400 \text{ Hz}$

The frequencies of the harmonics for an open pipe are given by $f_n = n f_1$, where $n = 1, 2, 3, \dots$

For the harmonic to fall within the audible range, its frequency must be less than or equal to $20{,}000 \text{ Hz}$:

$n \times 3400 \le 20{,}000$

$n \le \dfrac{20{,}000}{3400}$

$n \le 5.88$

Since $n$ must be an integer, the maximum possible value is $n = 5$.

Thus, the highest harmonic of this tube that falls within the audible range is $5$.