Reflected-Sound Doppler Shift and Echo Beats
For specular sound reflection in the classical low-speed regime, the reflector receives a Doppler-shifted frequency and reradiates that received frequency, so the return must be calculated by two sequential source-observer transformations.
Why this shows up in the exam
Echoes from walls and vehicles · Driver-hears-reflected-siren questions · Beat frequency from direct and returned sound
Learn the idea
Reflection from a moving body applies Doppler shift twice, once on reception and once on re-emission. A moving reflector first behaves like an observer receiving the incident sound and then like a source sending the reflected sound back.
🧠 Memory hook: A moving mirror Dopplers twice.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- f_return = f0 (v+u)/(v-u) — return to a stationary source from an approaching reflector of speed u
- f_beat = |f_return - f_direct| — beats between reflected and direct sounds
How to approach it
- 1Compute frequency received by the reflector
- 2Use that value as the reflected source frequency
- 3Compare with the direct signal if beats are requested
Common slip-ups that cost marks
- •Applying a single Doppler factor to a moving reflector
- •Treating a stationary wall as a moving observer
- •Comparing return frequency with the wrong direct tone
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A mass of 1 kg is attached to a spring of force constant 100 N/m. Find the angular frequency of small oscillations.
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