Final answer:
To find the fundamental frequency in an asymmetric pipe given two successive overtones, you divide the frequency of the first overtone by 3. The harmonics in a closed pipe are the odd multiples of the fundamental frequency.
Step-by-step explanation:
If you are given two successive frequencies of an asymmetric (closed at one end) pipe and need to find the fundamental frequency, it's important to understand that the overtone frequencies in such a pipe are not integer multiples of the fundamental frequency due to the harmonic series specific to closed pipes. In a pipe that is closed at one end, the harmonics are the odd multiples of the fundamental frequency. Given two successive frequencies, such as the first overtone (f2) and the second overtone (f3), we can use their values to determine the fundamental frequency (f1).
The relationship between the overtones in an asymmetric pipe and the fundamental frequency is given by:
f1 = f2/3 and f2 = f3/5,
where f2 and f3 are the first and second overtones, respectively. Because the tube is asymmetric, it has only the odd harmonics: f1 (the first harmonic or fundamental), f3 (the third harmonic or first overtone), and so on. To find the fundamental frequency, you can divide the frequency of the first overtone by 3 if you are given the first overtone and the second overtone.