An organ pipe closed at one end has fundamental frequency of 1500 Hz . The maximum number of overtones…

Frequency of audible overtones for an organ pipe closed at one end

The fundamental frequency is given by $f_1 = 1500 \ \text{Hz}$, and the upper limit of hearing is $19.5 \ \text{kHz} = 19500 \ \text{Hz}$. Since the pipe is closed at one end, only odd harmonics are present, with frequencies $f_n = n f_1$ where $n$ is an odd integer.

The maximum odd integer $n$ satisfying $n \cdot 1500 \leq 19500$ is $n \leq \frac{19500}{1500} = 13$.

Valid values of $n$ are $1, 3, 5, 7, 9, 11, 13$. The fundamental frequency $f_1$ is not an overtone, so the overtones correspond to $n = 3, 5, 7, 9, 11, 13$.

Counting gives 6 overtones within the audible range.

The maximum number of audible overtones is $\boxed{6}$.