A pipe has a length of 1m. Determine the frequencies of the fundamental and first two harmonics if the pipe is opened at both ends. (speed of sound in air = 340 m/s).
Explanation
To determine the frequencies of the fundamental and first two harmonics, we can use the formula:
f = v / (2L)
Where:
- f is the frequency of the harmonic
- v is the speed of sound in air
- L is the length of the pipe
Given that the length of the pipe is 1m and the speed of sound in air is 340 m/s, we can calculate the frequencies as follows:
For the fundamental frequency (first harmonic):
f1 = v / (2L)
= 340 m/s / (2 * 1m)
= 170 Hz
For the first overtone (second harmonic):
f2 = 2 * f1
= 2 * 170 Hz
= 340 Hz
For the second overtone (third harmonic):
f3 = 3 * f1
= 3 * 170 Hz
= 510 Hz
Therefore, the frequencies of the fundamental and first two harmonics for the pipe open at both ends are approximate:
- Fundamental frequency: 170 Hz
- First overtone: 340 Hz
- Second overtone: 510 Hz
