To calculate the wavelength and frequency of the first overtone and third harmonic in a closed pipe, we can use the formula:
c = 2Lf
Where:
c = speed of sound (approximately 343 m/s)
L = length of the pipe (converted to meters)
f = frequency
First, let's convert the length of the pipe from mm to meters:
L = 160 mm = 160/1000 m = 0.16 m
1) First overtone (second harmonic):
In the first overtone, we have one additional antinode compared to the fundamental mode. This means that the length of the pipe is half the wavelength.
Wavelength (λ) = 2L = 2 * 0.16 m = 0.32 m
To calculate the frequency, we rearrange the formula:
f = c / 2L = 343 m/s / (2 * 0.16 m) ≈ 1067.19 Hz
Therefore, the wavelength of the first overtone is 0.32 m and the frequency is approximately 1067.19 Hz.
2) Third harmonic:
In the third harmonic, there are two additional antinodes compared to the fundamental mode. This means that the length of the pipe is one-third of the wavelength.
Wavelength (λ) = 3L = 3 * 0.16 m = 0.48 m
To calculate the frequency:
f = c / λ = 343 m/s / 0.48 m ≈ 714.58 Hz
Therefore, the wavelength of the third harmonic is 0.48 m and the frequency is approximately 714.58 Hz.
The length of a closed pipe is 160 mm calculate the wavelength and the frequency of first overtone and third harmonic
1 answer