Waves & Sound
Two-source beats
Press Play — watch wavefronts interfere; the observer hears beats and y(t) shows the envelope.
Create beats from two slightly detuned wave sources. Hear and measure beat frequency as the difference between source frequencies.
Beats
Two sources with slightly different frequencies produce a beat pattern — a slow rise and fall in loudness.
Interference between f₁ and f₂ creates a combined wave whose amplitude modulates at |f₁ − f₂|. The observer hears the beat frequency.
- f_beat = |f₁ − f₂|
- Superposition of waves
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
Two speakers play tones that are almost the same frequency. A listener hears the loudness pulse up and down. What determines how fast it pulses?
Predictions to weigh
- The pulse rate equals the sum of the two frequencies.
- The pulse (beat) rate equals the difference between the two frequencies.
- The pulse rate equals the average of the two frequencies.
Variable roles
What you set:
- Source 1 frequency f₁ (Hz)
- Source 2 frequency f₂ (Hz)
What you measure:
- Carrier frequency f_c (Hz)
- Beat frequency f_beat (Hz)
How the investigation runs
- Open the two-source-beats preset and press Reset. Source 1 is fixed at 440 Hz.
- Enable the beat-frequency and carrier-frequency readouts at the observer.
- Set Source 2's frequency for each trial and record the beat frequency.
Governing equation
Beat Frequency — f_beat = |f₁ − f₂|
When two tones of nearly equal frequency overlap, their interference pattern pulses in loudness at a rate equal to the difference between the two frequencies.
Carrier Frequency — f_c = (f₁ + f₂)/2
The pitch a listener actually perceives is close to the average of the two source frequencies — the beat is a slow amplitude pulsation riding on top of that average tone.
What the printable worksheet asks students to work out
- For one trial, compute f_beat = |f₂ − f₁| and f_c = (f₁ + f₂)/2. Compare both to the table.
- Explain why a listener perceives one tone near the carrier frequency, with loudness pulsing at the (much slower) beat frequency.
Where this shows up beyond the lab
- Musicians tune instruments by listening for beats between their note and a reference tone, adjusting until the beats slow to zero. Explain why zero beats means the two frequencies are exactly equal.
- As f₂ gets closer and closer to f₁, what happens to the beat frequency? What would you hear in the limit f₂ = f₁?
- AP Physics 2 — Unit 14: Waves, Sound, and Physical Optics
- IB Physics — C.3 Wave phenomena
- General High School Physics — Waves & sound
- NGSS High School Physics — Wave properties
- Welcome to Two Source Beats
- Select the observer
- Press Play
- Hear the wobble
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.