Question

Find the fundamental frequency and the frequencies of the first two overtones of a pipe $45.0cm$ long, if the pipe is open at both ends.

Answer 1

The natural frequency, or fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency or base frequency of a periodic waveform. The fundamental frequency is also a supply frequency. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal.

Complete step by step answer:
Frequency the number of waves that pass a fixed point in unit time; also, the number of cycles or vibrations undergone during one unit of time by a body in periodic motion. A body in periodic motion is said to have undergone one cycle or one vibration after passing through a series of events or positions and returning to its original state.
$V =$Wave Velocity
$L =$ Length of string
${f_1} =$ Fundamental frequency
${f_2} =$ First overtone or Second harmonic
${f_3} =$ Second overtone or third harmonic
Harmonics are of three type

1. Positive sequence harmonics: a positive sequence harmonic rotates in the direction of fundamental frequency.
2. Negative sequence harmonics: a negative sequence harmonic rotates in direction opposite to the fundamental frequency.
3. Zero sequence harmonics: zero sequence harmonics does not rotate with fundamental frequency; therefore, it is called zero frequency. Alternative current varies sinusoidally at a particular frequency called the fundamental frequency which is usually $50Hz$ or $60Hz$. Current harmonics are used in switching transformers, discharge lighting, refrigerator, computer and data processing loads, saturated magnetic device, ballast of fluorescent, etc.
   We have,
   $V = 344m/\sec ,L = 45cm = 0.45m$
   Fundamental frequency is given by,
   ${f_1} = \dfrac{V}{{2L}} = \dfrac{{344}}{{2 \times 0.45}}$
   $= 382.2Hz$
   Therefore, the frequency of first overtone,
   ${f_2} = 2{f_1} = 2 \times 382.2 = 764.4Hz$
   Frequency of second overtone is,
   ${f_3} = 3{f_1} = 3 \times 382.2 = 1146Hz$

Note:
Harmonics are defined as unwanted higher frequency components that are integral multiples of fundamental frequency.
Harmonics has lower amplitude than the fundamental frequency.
The number of cycles completed by any wave per second is called frequency. Frequency is inversely proportional to time.