Calculating Wavelength of Harmonics Calculator

Calculator

System type

Mode step

Length value

Length unit

Wave speed

Speed unit

Series rows

Series output

Generate harmonic series table and graph

Notes

For closed-open air columns, only odd harmonics appear.

Example Data Table

System	Length (m)	Wave speed (m/s)	Mode step	Harmonic	Wavelength (m)	Frequency (Hz)
String or fixed-fixed boundary	1.20	120.00	3	3rd harmonic	0.800000	150.000000
Open-open air column	0.90	343.00	2	2nd harmonic	0.900000	381.111111
Closed-open air column	0.85	343.00	2	3rd harmonic	1.133333	302.647059

Formula Used

Harmonic wavelength depends on the boundary condition of the system. Strings fixed at both ends and open-open air columns share one wavelength rule. Closed-open air columns use only odd harmonics.

1) String or fixed-fixed boundary

λ_n = 2L / n

f_n = nv / 2L

2) Open-open air column

λ_n = 2L / n

f_n = nv / 2L

3) Closed-open air column

λ_n = 4L / (2n - 1)

f_n = (2n - 1)v / 4L

Supporting relations

f = v / λ

ω = 2πf

k = 2π / λ

Here, L is the resonating length, v is wave speed, n is the selected mode step, λ is wavelength, f is frequency, ω is angular frequency, and k is wave number.

How to Use This Calculator

Select the system type that matches your problem.
Enter the physical length of the string or air column.
Choose the matching input unit for that length.
Enter the wave speed in your preferred speed unit.
Set the mode step. For closed-open columns, step 1 means the 1st harmonic, step 2 means the 3rd harmonic, and so on.
Enable the series option when you want multiple harmonic rows and a graph.
Press Calculate to display the result section above the form.
Use the CSV or PDF buttons to export the displayed result data.

FAQs

1. What does harmonic wavelength mean?

It is the wavelength associated with a standing-wave mode in a string or air column. Each allowed mode fits the system length using specific boundary conditions.

2. Why do closed-open pipes use odd harmonics only?

One end is a node and the other is an antinode. That boundary pattern only supports modes with odd quarter-wavelength combinations inside the pipe.

3. Is the formula the same for strings and open-open pipes?

Yes. Both support wavelengths given by 2L divided by the harmonic number. Their frequency relation also follows the same pattern when wave speed is known.

4. What wave speed should I enter?

Enter the speed relevant to your medium. For air, many examples use about 343 m/s near room temperature. For strings, speed depends on tension and linear density.

5. What is the difference between mode step and harmonic label here?

For strings and open-open columns, they match directly. For closed-open columns, step 2 corresponds to the 3rd harmonic because even harmonics are absent.

6. Why does wavelength get smaller at higher harmonics?

Higher modes fit more segments into the same physical length. Since the length is fixed, each allowed wavelength becomes shorter as the harmonic order increases.

7. Can I use feet or inches instead of meters?

Yes. The calculator converts supported length units into meters internally. That helps keep the formulas consistent while still allowing flexible user inputs.

8. What do angular frequency and wave number show?

Angular frequency shows oscillation rate in radians per second. Wave number shows spatial repetition in radians per meter. Both are useful in wave equations.