Phoebe guidesA technician must decide whether speed of sound is safe before changing classroom temperature on the real device. The result is unresolved until the rule and units are checked. Predict the direction first.
See the relationship before changing it
The figure reads from left to right. The blue card is classroom temperature. The middle card applies this page's rule. The green card is speed of sound. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only classroom temperature, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 22 degrees C.
- 2
Name the relationship. speed = 331.3 m/s + 0.606 x temperature
- 3
Substitute with units. 331.3 + 0.606 x 22 = 344.6 m/s
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change classroom temperature
Try Predict the direction of speed = 331.3 m/s + 0.606 x temperature. Test another classroom temperature, then compare speed of sound.
Observe Warmer air raises the speed used to convert echo time into distance. Reset classroom temperature to 22 and compare speed of sound.
Explain Warmer air raises the speed used to convert echo time into distance.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Sound speed is an input
The sensor measures time, not distance. Air temperature changes how far sound travels during the measured interval.
2. Undo the round trip
Estimate sound speedv=331.3+0.606T m/s.
Multiply speed by timevt is the full out-and-back path.
Divide by twod=vt/2 is the one-way range.
3. Add motion and a second reflector
The factor two in Doppler comes from the outbound and return paths. A second surface produces a second correct delay rather than “random sensor noise.”
4. Try the room temperature
TryMove the classroom temperature while holding the measured delays and motion fixed.
ObserveAt 22 °C, sound travels at 344.6 m/s, the 2.00 ms echo means 34.5 cm, the Doppler shift is about 116 Hz, and the second surface returns at 3.48 ms.
ExplainAll four readouts reuse the same temperature-dependent sound speed, so changing temperature changes range, Doppler, and multipath timing together.
This linear sound-speed approximation assumes ordinary air.
- Real transducers have beam patterns, ring-down, thresholds, dead zones, humidity sensitivity, finite bandwidth, surface-angle effects, and echo-selection firmware
- Needs separate evidence
Use field evidence or a deeper model before release.
5. Compare echoes, not just readings
The expected desk target returns near 2.00 ms. A later 3.48 ms return fits a real 0.60 m reflector, so the report should preserve the echo pattern rather than deleting it as an outlier.
6. State the safe claim
The bench supports a temperature-tagged range and motion observation for this setup. It does not prove object identity, continuous tracking, or one-path propagation.
7. Check yourself
Why divide the echo path by two?
Why is Doppler doubled here?
Is a 3.48 ms echo automatically noise?
These are the chapter inputs, worked results, and named teaching assumptions.
- 22 °C
- Temperature or angle value
- 344.6 m/s
- Time, interval, or service-life value
- 2.00 ms
- Time, interval, or service-life value
- 34.5 cm
- Distance, wavelength, or size
- 40 kHz
- Frequency, sample rate, or event rate
- 0.5 m/s
- Time, interval, or service-life value
- 116 Hz
- Frequency, sample rate, or event rate
- 0.60 m
- Distance, wavelength, or size
- 3.48 ms
- Time, interval, or service-life value
They do not model the complete acoustic scene; Under the Hood keeps those limits.