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Concept module

Beats

Superpose two nearby sound frequencies, watch the fast carrier sit inside a slower envelope, and connect beat rate to the frequency difference on one compact bench.

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Starter track

Step 3 of 50 / 5 complete

Sound and Acoustics

Earlier steps still set up Beats.

1. Sound Waves and Longitudinal Motion2. Pitch, Frequency, and Loudness / Intensity3. Beats4. Doppler Effect+1 more steps

Previous step: Pitch, Frequency, and Loudness / Intensity.

Also in Waves.

Start from track beginning

Why it behaves this way

Explanation

Beats appear when two nearby frequencies reach the same listener or probe and superpose. The fast oscillation does not disappear. Instead, it sits inside a slower amplitude envelope, so the combined motion swells and fades even though each source keeps oscillating steadily at its own frequency.

This bench stays bounded on purpose. It shows two equal-amplitude source traces, one live resultant, and one normalized loudness cue from the same superposition state. That keeps the physics honest: beat frequency comes from the frequency difference, while the faster carrier still follows the average source frequency.

Key ideas

01Beat frequency depends on the difference between the two source frequencies, not on their average amplitude or on the average frequency by itself.

02The loud-soft pulse is an envelope created by superposition, so neither source needs to get louder or quieter on its own.

03Keeping the same frequency difference keeps the same beat rate even if both source frequencies shift upward or downward together.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

These checks read the same source frequencies and live envelope state that the stage and graphs already show, so the math stays tied to one superposition bench.

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Frozen valuesUsing frozen parameters

For the current sources with $f_{1} = 1 Hz$ and $f_{2} = 1.12 Hz$ , what beat frequency and average carrier frequency follow from that pair?

f_{1}

Source A frequency

1 Hz

f_{2}

Source B frequency

1.12 Hz

f_{b e a t}

Beat frequency

0.12 Hz

f_{a v g}

Average carrier frequency

1.06 Hz

1. Start from the nearby-frequency relations

Use

f_{b e a t} = ∣ f_{2} - f_{1} ∣

for the envelope rate and

f_{a v g} = \frac{f _{1} + f _{2}}{2}

for the faster carrier underneath it.

2. Substitute the live source pair

f_{b e a t} = ∣1.12 - 1∣ = 0.12 Hz

and

f_{a v g} = \frac{1 + 1.12}{2} = 1.06 Hz

3. Interpret the pulse rate

So the envelope repeats at

0.12 Hz

and each loud-soft cycle takes

8.33 s

while the faster oscillation still centers on

1.06 Hz

Current beat pair

f_{b e a t} = 0.12 Hz, f_{a v g} = 1.06 Hz

The frequency difference is small, so the carrier oscillates many times before the loudness envelope completes one slow beat cycle.

Envelope checkpoint

You want the loud-soft pulsing to disappear without changing the source amplitudes. What should you do to the two source frequencies?

Make a prediction before you reveal the next step.

Decide whether you should move them farther apart, bring them together, or shift both upward together.

Check your reasoning against the live bench.

Bring the two source frequencies together until they match.

The beat envelope comes from the frequency difference. When

f_{1}

and

f_{2}

become equal,

Δ f

goes to zero and the separate beat cycle disappears.

Common misconception

If you hear beats, each source must be turning its own volume up and down.

Each source keeps a steady amplitude in this model. The pulsing comes from how the two waves add together.

The superposed resultant grows when the waves reinforce and shrinks when they nearly cancel, which is why the loudness cue pulses.

Quick test

Variable effect

Question 1 of 4

Use the live bench, not memory alone. These checks separate beat rate, carrier frequency, and source amplitude.

Which quantity sets the beat frequency in this page's model?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows two source drivers on the left, a shared time-trace region in the middle, and one listener cue on the right. The upper trace compares the two source motions, while the lower trace shows their combined resultant with an optional envelope guide around it.

Optional overlays label the envelope, the loudness cue, and the current frequency difference. In compare mode, the same compact bench appears in two rows so the learner can contrast beat rate and carrier frequency without leaving the shared layout.

Graph summary

The first graph plots Source A, Source B, and the resultant displacement against time so the faster carrier stays visible inside the superposition.

The second graph plots the normalized envelope ratio and a bounded loudness cue against time so the slow beat cycle can be read separately from the fast oscillation.

Carry beats into superposition and resonance

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Motion and pitchOscillations

Beats

Sound and Acoustics

Explanation

Step through the frozen example

For the current sources with $f_{1} = 1 Hz$ and $f_{2} = 1.12 Hz$ , what beat frequency and average carrier frequency follow from that pair?

Which quantity sets the beat frequency in this page's model?

Keep this idea moving

Doppler Effect

Wave Interference

Standing Waves

Beats

Sound and Acoustics

Explanation

Step through the frozen example

For the current sources with f1​=1Hz and f2​=1.12Hz, what beat frequency and average carrier frequency follow from that pair?

Which quantity sets the beat frequency in this page's model?

Keep this idea moving

Doppler Effect

Wave Interference

Standing Waves

For the current sources with $f_{1} = 1 Hz$ and $f_{2} = 1.12 Hz$ , what beat frequency and average carrier frequency follow from that pair?