Lab Methods - Graph

The gain of an amplifier is plotted versus angular frequency ω in the diagram above. If K and a are positive constants, the frequency dependence of the gain near ω = 3 × 10⁵ second⁻¹ is most accurately expressed by

A. Ke^−aω
B. Kω²
C. Kω
D. Kω⁻¹
E. Kω⁻²

(GR8677 #39)

Solution:

(A) g = Ke^−aω → decreasing (exponential decay). FALSE.


(B) g = Kω² → increasing (quadratic function/parabola). FALSE.


(C) g = Kω → increasing (linear function). FALSE.
(D) g = K/ω → decreasing (linear function). FALSE.

(E) g = K/ω² → decreasing (quadratic function). TRUE.

Check:
At ω = 10⁶, g ≈ 10
g = K/ω² 
10 = K/10¹²
K = 10¹³

At ω = 3 × 10⁵, K = 10¹³
g = 10¹³/(9 × 10¹⁰) ≈ 0.11 × 10³
10²  g  10³

Answer: E