HC-SR04 Physics

Learning Goals 5 min

1. Explain how the HC-SR04 ultrasonic sensor measures distance: send a sound pulse, time the echo, divide.
2. State the speed of sound at room temperature (~343 m/s, or roughly 29 microseconds per centimetre, one way) and use it to predict echo times for known distances.
3. Identify the limits of an ultrasonic sensor — minimum range, maximum range, beam angle, what materials it can't see — before you wire a single thing.

Warm-Up 10 min

Cluster D opens with the HC-SR04 — the little blue board with two silver cylinders that look like robot eyes. They're not eyes; they're a tiny speaker and a tiny microphone, both working at 40 kHz — far above what humans can hear. The sketch shouts at a wall in ultrasound, listens for the echo, and uses the time-of-flight to compute how far away the wall is.

An everyday analogy

Bats do exactly this. So do submarines. So do reversing cars (the "beep beep beep" that speeds up as you approach a kerb is an HC-SR04's big, expensive cousin). The principle:

1. Send a short, sharp sound.
2. Start a stopwatch.
3. Stop the stopwatch when the echo arrives.
4. Distance = (time × speed of sound) ÷ 2.

Divide by 2 because the sound travelled out and back. We'll spend today on the physics; tomorrow on the pulseIn() function that actually does the timing in code; the day after on the distance maths.

New Concept · Time-of-flight measurement 25 min

The four-pin module

Two control wires — TRIG (you talk to it) and ECHO (it talks back). Plus power and ground.

What happens during a single measurement

1. You set TRIG HIGH for 10 microseconds, then LOW. This tells the chip to start.
2. The chip blasts an 8-cycle 40 kHz "ping" out of the transmit cylinder.
3. The chip immediately raises ECHO HIGH and starts its own internal stopwatch.
4. The ping travels through the air, hits something, and bounces back.
5. The receive cylinder picks up the returning ping.
6. The chip drops ECHO LOW.

So the width of the ECHO pulse — the time it stayed HIGH — equals the round-trip time of the ping. Measuring that pulse width is what tomorrow's lesson (pulseIn()) is about. Today is the physics.

The speed of sound — the magic constant

At 20 °C in dry air, sound travels at 343 metres per second. Some equivalent forms that are handy to memorise:

• 343 m/s = 34 300 cm/s = 34.3 cm per millisecond = 0.0343 cm per microsecond.
• Inverted: ~29.1 microseconds per centimetre, one way.
• For a round trip: ~58 microseconds per centimetre.

That 58 µs/cm is the number we'll plug into the distance formula in two days. For now, memorise it — it's the bridge between the time the chip reports and the distance you want.

Worked numerical examples

If the object is 10 cm away:

time = distance × 58 µs/cm
     = 10 × 58
     = 580 µs

So ECHO stays HIGH for 580 microseconds.

If ECHO reports 1740 µs:

distance = time / 58
         = 1740 / 58
         = 30 cm

That's really the whole physics of the sensor: multiply (or divide) by 58.

Where the speed of sound varies

Speed depends slightly on temperature: warmer air = faster sound. The precise formula:

v (m/s) = 331.4 + 0.6 × T(°C)

At 20 °C → 343.4 m/s. At 30 °C → 349.4 m/s (1.7% faster). At −10 °C → 325.4 m/s (5% slower).

For classroom Malaysia (25–30 °C), using a fixed 343 m/s overestimates distance by ~1%. For a 30 cm reading, that's a 3 mm error — well below our other error sources. Ignore it for now; revisit if you ever build a precision rangefinder.

Limits of the sensor

• Minimum range: ~2 cm. Closer than that, the ping and echo overlap and the chip gets confused.
• Maximum range: ~400 cm (4 m) in lab conditions, more like 2–3 m in practice. Beyond that the echo is too weak to detect.
• Beam angle: the ping spreads in a ~15° cone. Anything outside that cone won't be seen, even if it's nearby. Anything inside competes — closest wins.
• Soft / fluffy / angled surfaces absorb or deflect the ping and produce no usable echo. Curtains, foam, the side of a tilted book — all invisible.
• Hard, flat, perpendicular surfaces give the strongest echo. A wall, a textbook held flat, a metal sheet — all easy.

Worked Example · Predict the echo times 15 min

No wiring today — we're building intuition before code. Work through these as a class, on paper or a whiteboard. The point is to feel comfortable converting between time and distance before you ever touch pulseIn().

Predictions to compute

1. Object 5 cm in front of the sensor → ECHO pulse width is ___ µs.
2. Object 50 cm in front of the sensor → ECHO pulse width is ___ µs.
3. Object 100 cm in front of the sensor → ECHO pulse width is ___ µs.
4. Object 1 metre in front of the sensor → ECHO pulse width is ___ ms (note units!).
5. Object at the maximum range (4 m) → ECHO pulse width is ___ ms.

Reverse predictions

The sensor reports ECHO pulse widths. Convert these to distances:

1. ECHO = 1160 µs → distance = ___ cm
2. ECHO = 4640 µs → distance = ___ cm
3. ECHO = 11 600 µs → distance = ___ cm (or m)
4. ECHO = 38 000 µs → distance = ___ cm — and is this within the sensor's range?

The reflection table

Predict which of these targets would give a strong echo, a weak one, or none at all. Discuss as a class.

Try It Yourself 15 min

v = 331.4 + 0.6 × 30 = 349.4 m/s = 34 940 cm/s
1 cm round-trip: 2 / 34 940 × 1 000 000 = 57.24 µs/cm
Error: (58 - 57.24) / 57.24 = 1.3%

Mini-Challenge · Build a paper rangefinder calculator 15 min

Today is theory day, so today's challenge is theory too. In pairs, design (on paper) a short reference card that someone could tape to their lab bench to help them debug an HC-SR04 sketch quickly. The card should have:

1. The conversion formula, in both directions: µs → cm and cm → µs.
2. A small table of 5 common distances (5, 10, 25, 50, 100 cm) with their predicted ECHO times.
3. A "limits" box: minimum range, maximum range, beam angle.
4. A "what could go wrong" box with three bullet points (sensor sees the floor, sensor saturates near the wall, sensor sees nothing because target is soft, etc.).

Aim for a card that fits on half a sheet of A4. Hand-drawn is fine — the point is the content, not the visuals.

It's done when:

• A classmate (not your partner) can read the card and use it to predict an ECHO time for a 1.5 m distance without asking you for help.
• The "what could go wrong" box mentions at least one material the sensor can't see.
• You can hand the card to a teacher who's never seen an ultrasonic sensor and they understand the rules within a minute.

Recap 5 min

The HC-SR04 measures distance using sound's round-trip time. You trigger a ping with a 10 µs pulse on TRIG, and the chip raises ECHO for exactly as long as the round-trip took. At 343 m/s (the speed of sound at 20 °C), the conversion is ~58 µs per centimetre round-trip — the single number you need to memorise. The sensor works best on hard, flat, perpendicular surfaces; struggles with soft, angled, or absorbent targets; and is bounded to roughly 2 cm minimum and 4 m maximum. Tomorrow we use pulseIn() to measure that ECHO pulse in code; the day after we wrap the whole thing in a clean distance function.

Ultrasonic

Sound waves above human hearing — typically above 20 kHz. The HC-SR04 uses 40 kHz, well clear of human (and most pet) hearing.

Time-of-flight (TOF)

Measuring distance by timing how long a signal takes to reach an object and return. Used by ultrasonic, laser, radar.

Round-trip time

How long it takes a pulse to travel out and bounce back — what ECHO reports. Always twice the one-way travel time.

TRIG / ECHO

The HC-SR04's two control pins. You pulse TRIG HIGH for 10 µs to start; the chip pulses ECHO HIGH for the duration of the round trip.

Beam angle

The cone of space the sensor "sees". For the HC-SR04 it's ~15° wide. Anything outside the cone is invisible; anything inside competes — closest wins.

Acoustic absorption

The tendency of soft, fluffy materials to absorb sound energy rather than reflect it. Why curtains, foam and cats are hard targets.

Speed of sound (in air)

~343 m/s at 20 °C, increasing by ~0.6 m/s per °C. We use the 20 °C value (= 58 µs/cm round-trip) as a good-enough constant.

Minimum / maximum range

The HC-SR04 is reliable from ~2 cm to ~400 cm. Below 2 cm: ping and echo overlap. Above 400 cm: echo too weak to detect.

Homework 5 min

Conversion drill. Work through these on paper — show the multiplication or division each time, not just the answer:

1. An object is 12 cm in front of the sensor. ECHO pulse width = ?
2. An object is 75 cm in front of the sensor. ECHO pulse width = ?
3. An object is 2.5 m in front of the sensor. ECHO pulse width = ?
4. ECHO reports 2320 µs. Distance = ?
5. ECHO reports 14 500 µs. Distance = ? Is this within the sensor's range?
6. ECHO reports 87 µs. Distance = ? Is this within the sensor's range?
7. Bonus: The temperature is 40 °C (a hot day in the sun). Recompute (3) using the temperature-corrected speed of sound, and compare to your original answer. By how many millimetres do they differ?

Bring back next class:

• Your 7 worked answers (with the maths shown).
• Your reference card from the mini-challenge (or a fresh polished version).
• No sketch this lesson — tomorrow we write the first one.