To determine the frequencies of the first two harmonics in a pipe filled with gas, we need to consider the relationship between the length of the pipe and the wavelength of the sound waves produced.
In an open-open pipe (which is the case when a pipe is open at one end), the fundamental frequency, or the first harmonic, is given by the formula:
f1 = v / (2L),
where f1 is the fundamental frequency, v is the speed of sound in the gas, and L is the length of the pipe.
Using the given values, we can calculate the frequency of the fundamental tone:
f1 = 300 m/s / (2 * 0.6 m) = 250 Hz.
The first harmonic, or fundamental frequency, is 250 Hz.
For an open-open pipe, the second harmonic, or the first overtone, occurs at twice the frequency of the fundamental tone. Therefore, the frequency of the second harmonic, f2, can be calculated as:
f2 = 2 * f1 = 2 * 250 Hz = 500 Hz.
Hence, the frequencies of the first two harmonics in this particular open-open pipe are 250 Hz and 500 Hz, respectively.