Vọng âm Doppler và biên sóng đứng
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| Doppler/ˈdɒplə/ | The shift in observed frequency caused by motion of source or observer. |
| antinode/ˌæntɪˈnəʊd/ | A position of maximum oscillation amplitude in a standing wave. |
| fundamental/ˌfʌndəˈmentl/ | The lowest resonant frequency of a system. |
An echo shifted twice
- A driver sounds a 500 Hz siren while approaching a wall. The echo comes back at about 530 Hz: the sound was Doppler 多普勒-shifted on the way out and again on the way back.
- GRE waves questions test acoustic Doppler shifts, echoes and standing waves in pipes.
Source moving or observer moving
- Speeds are relative to the air. Source approaching a still observer: $f' = f\dfrac{c}{c - u_s}$. Observer approaching a still source: $f' = f\dfrac{c + u_o}{c}$.
- These are not symmetric; receding flips the sign of the speed.
The source and observer formulas are not interchangeable: a source approaching at $u$ and an observer approaching at $u$ give different shifts.
A listener runs at 34 m/s toward a stationary 680 Hz source ($c = 340$ m/s). Frequency heard in Hz?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
A moving observer hears $f(c + v_o)/c = 680 \times 374/340 = 748$ Hz.
Echo from a fixed wall
- The wall receives $f\dfrac{c}{c - u}$ and re-emits it unchanged; the approaching driver hears $f\dfrac{c + u}{c - u}$.
$f = 500$ Hz, $u = 10$ m/s, $c = 340$ m/s: $500 \times \tfrac{350}{330} \approx 530.3$ Hz. For small $u/c$ the fractional shift is about $2u/c$.
A 400 Hz siren approaches a fixed wall at 20 m/s ($c = 340$ m/s). Echo frequency heard by the driver in Hz?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
The wall receives $400 \times 340/(340 - 20) = 425$ Hz and reflects it; the approaching driver hears $425 \times (340 + 20)/340 = 450$ Hz.
Pipes: nodes and antinodes 波腹
- Open end: displacement antinode. Closed end: displacement node.
- Both open: $f_n = \dfrac{nc}{2L}$, all $n$. One closed: $f_n = \dfrac{(2n - 1)c}{4L}$, odd multiples only.
A 0.50 m pipe closed at one end, $c = 340$ m/s. Fundamental in Hz?
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A pipe closed at one end is a quarter wavelength long at its fundamental: $f = c/4L = 340/2 = 170$ Hz.
The next resonance of that closed pipe above 170 Hz is
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
A closed pipe has only odd harmonics, so after 170 Hz comes $3 \times 170 = 510$ Hz.
Closing one end
- A 0.85 m pipe in 340 m/s air: both open gives 200, 400, 600 Hz. Closing one end gives 100, 300, 500 Hz.
- The fundamental 基频 halves, and none of the old frequencies survives: they are even multiples of $c/4L$.
Which pipe resonates?
Distinguish open–open and open–closed resonances.
Closing one end of an open pipe halves its fundamental frequency and leaves only odd harmonics.
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
True. The fundamental changes from $c/2L$ to $c/4L$, and a closed–open pipe supports only odd multiples of it.
Recap
- Source and observer formulas differ; measure speeds relative to the medium.
- Echo from a fixed wall: $f(c + u)/(c - u)$.
- Open–open: $nc/2L$; open–closed: odd multiples of $c/4L$.
- Doppler: The shift in observed frequency caused by motion of source or observer.
- fundamental: The lowest resonant frequency of a system.