Audio Frequency Calculator

Example Data

Formulas Used

• From period: f = 1 / T
• From wavelength: f = v / λ where v is wave speed.
• From angular frequency: f = ω / (2π)
• Beat frequency: f_beat = |f₁ − f₂|
• Doppler shift:
  Approaching: f′ = f · (v + v_o) / (v − v_s)
  Receding: f′ = f · (v − v_o) / (v + v_s)
• Equal temperament note mapping: nearest MIDI note n = round(69 + 12·log₂(f/A4))

Air speed approximation: v ≈ 331.3 + 0.606·T(°C) m/s.

How to Use This Calculator

1. Select a calculation mode that matches your known values.
2. Enter the inputs, choosing units where provided.
3. For wavelength or Doppler, choose a medium or custom speed.
4. Click Calculate to see results above the form.
5. Use Download CSV or Download PDF for reports.

Understanding Audio Frequency

Audio frequency describes how many pressure cycles occur each second in a sound wave, measured in hertz (Hz). Human hearing is often quoted as 20 Hz to 20,000 Hz, while speech energy sits mainly between 85 Hz and 4,000 Hz. Sub‑bass sits near 20–60 Hz, and presence peaks fall around 2–5 kHz. This calculator helps convert among common ways audio frequency is specified.

Period and Frequency Conversion

If you know the period, the frequency is f = 1/T. A 1 millisecond period corresponds to 1,000 Hz, and a 10 microsecond period corresponds to 100,000 Hz. Because audio work often mixes milliseconds, microseconds, and seconds, unit-aware conversion prevents factor‑of‑1,000 mistakes.

Wavelength from Speed of Sound

Wavelength links pitch to physical spacing: λ = v/f. In air at about 20°C, v ≈ 343 m/s, so a 440 Hz tone has λ ≈ 0.78 m. In water (≈1,480 m/s) the same tone stretches to ≈3.36 m. Select a medium or enter a custom speed for accuracy.

Harmonics and Musical Notes

Musical instruments produce harmonics at integer multiples: 2f, 3f, 4f, and so on. If a guitar string’s fundamental is 110 Hz (A2), the second harmonic is 220 Hz (A3) and the fourth is 440 Hz (A4). The note mapping tool estimates the nearest equal‑temperament pitch.

Sampling Rate and Nyquist Check

Digital audio needs a sampling rate at least twice the highest frequency you want to capture (Nyquist). For 20 kHz content, 44.1 kHz provides a 22.05 kHz Nyquist limit, and 48 kHz provides 24 kHz. Use the calculator to confirm whether your sample rate is adequate for a target band.

Doppler Shift for Moving Sources

Relative motion shifts perceived pitch. A siren at 1,000 Hz moving toward you can sound higher by several percent, depending on source and observer speeds. This calculator uses standard Doppler formulas with a selectable sound speed, letting you test scenarios such as vehicles, drones, or rotating machinery.

Practical Audio Troubleshooting

Frequency calculations support real tasks: finding mains hum (50/60 Hz), diagnosing resonance peaks, sizing acoustic panels by wavelength, or checking crossover points in speakers. When results look wrong, verify units, confirm medium speed, and ensure you are using fundamental frequency rather than a harmonic. Sweep tones in 1/3‑octave steps to locate problem bands.

FAQs

1. What is the difference between frequency and pitch?

Frequency is a physical measurement in hertz. Pitch is the brain’s perception of that frequency and can shift with loudness, context, and harmonics. Two sounds can share a fundamental frequency yet feel different due to their harmonic content.

2. How do I convert milliseconds to hertz?

Convert the period to seconds first, then use f = 1/T. For example, 2 ms = 0.002 s, so f = 1/0.002 = 500 Hz. The calculator handles unit conversion automatically.

3. Why does wavelength change with the medium?

Wavelength depends on wave speed: λ = v/f. Frequency is set by the source, but speed changes in air, water, and solids, so the spacing between wave peaks changes. That is why the same tone has different wavelengths in different media.

4. What sampling rate do I need for a target frequency?

Use at least 2× the highest frequency you want to record. For example, to capture up to 18 kHz, choose 36 kHz or higher; common choices are 44.1 kHz or 48 kHz. Extra headroom supports filter design.

5. How accurate is the Doppler shift result?

Accuracy depends on how well the chosen sound speed matches your situation. Air temperature, wind, and whether motion is directly toward/away affect results. Use the custom speed option and realistic velocities for the best estimate.

6. Can I use this for machinery vibration analysis?

Yes. Enter rotational speed or measured periods to compute frequency, then compare with expected harmonics or fault-related bands. Pair results with spectra from your measurement tool to confirm peaks and avoid confusing a harmonic with the fundamental.