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).

170 Hz, 340 Hz, 510 Hz

120 Hz, 220 Hz, 390 Hz

90 Hz, 230 Hz, 440 Hz

210 Hz, 410 Hz, 510 Hz

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