Speakers & Projectors – Computer Fundamentals & Hardware
(NCO – Cyber Olympiad – IIT‑JEE / competitive level)
Goal – Provide a compact, exam‑ready reference that covers the physics, engineering, and design trade‑offs of audio‑output (speakers) and visual‑output (projectors) systems.
1. Quick Overview
| Device | Primary Function | Key Sub‑Systems | Typical Output |
|---|---|---|---|
| Speaker | Convert electrical audio signals into sound waves | Voice coil, magnet, diaphragm, crossover, amplifier | 20 Hz–20 kHz, 20 dB–120 dB SPL |
| Projector | Convert digital video into a visible image on a screen | Light source, image‑processing unit, lens, color wheel (or color‑separating optics), screen | 720p–4K, 250–5000 cd/m² brightness |
2. Speakers
2.1 Types of Drivers
| Driver | Working Principle | Advantages | Disadvantages |
|---|---|---|---|
| Dynamic (Moving‑coil) | Voice coil moves in a magnetic field → diaphragm motion | Cheap, wide frequency response | Susceptible to distortion at high SPL |
| Electrostatic | Thin diaphragm between plates → electrostatic force | Very flat response, low distortion | Requires high‑voltage driver, limited power |
| Piezoelectric | Piezo crystal expands → mechanical motion | Small, low power, high frequency | Limited low‑frequency response |
| Electrodynamic (Magnet‑less) | Uses permanent magnet + moving coil | No magnetic field, high safety | Expensive, limited power |
2.2 Core Physics
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Voice‑coil equation
[ F = B \cdot L \cdot I ]- (F) – force on the coil
- (B) – magnetic flux density (T)
- (L) – length of wire in magnetic field (m)
- (I) – current (A)
-
Mechanical dynamics
[ F = m \ddot{x} + R \dot{x} + k x ]- (m) – mass of the diaphragm
- (R) – mechanical damping
- (k) – stiffness (spring constant)
- (x) – displacement
The intersection of electrical and mechanical dynamics gives the resonant frequency (f_0) of the driver (≈ 50–200 Hz for woofers).
2.3 Power Handling & Impedance
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Impedance (Z) is the load seen by the amplifier.
[ Z = R + j\omega L - \frac{j}{\omega C} ]- For a pure resistive driver (most mid‑range/woofers) (Z \approx R).
-
Power dissipation
[ P = \frac{V^2}{R} = I^2 R = V I ]- (V) – RMS voltage across driver
- (I) – RMS current through driver
2.4 Loudness & SPL
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Sound Pressure Level (SPL) (dB)
[ \text{SPL} = 20 \log_{10}!\left(\frac{p}{p_0}\right) ]- (p) – sound pressure (Pa)
- (p_0 = 20;\mu\text{Pa}) (threshold of hearing)
-
Sensitivity (SPL at 1 m for 1 W input)
[ \text{SPL}{\text{sens}} = 20 \log{10}!\left(\frac{V_{\text{out}}}{1,\text{V}}\right) + 94 ]- Typical: 88–96 dB
-
Required input power for desired SPL
[ P_{\text{in}} = 10^{\frac{\text{SPL}{\text{desired}} - \text{SPL}{\text{sens}}}{20}} ]
2.5 Crossover Networks
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Purpose – divide audio spectrum between drivers (woofer, tweeter, mid‑range).
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Basic 2‑way:
[ H_{\text{low}}(s) = \frac{1}{1 + s \frac{R}{\omega_c L} + (s\tau)^2} ]- (\omega_c = 2\pi f_c) – cutoff frequency
- (\tau) – time constant (usually (\tau = R C))
-
Key design points
- Filter order – steeper roll‑off