Lab Methods - Graph

In laboratory experiments, graph are employed to determine how one measured variable depends on another. These graphs generally fall into three categories: linear, semilog (logarithmic versus linear), and log-log. Which type of graph listed in the third column below would NOT be the best for plotting data to test the relationship given in the first and second columns?

		Relation		Variables Plotted		Type of graph
A.		dN/dt ∝ e−2t		Activity vs time for a radioactive isotope		Semilog
B.		eVs = hf  − W		Stopping potential vs frequency for the photoelectric effect		Linear
C.		s ∝ t2		Distance vs time for an object undergoing constant acceleration		Log-log
D.		Vout/Vin ∝ 1/ω		Gain vs frequency for a low-pass filter		Linear
E.		P ∝ T4		Power radiated vs temperature for blackbody radiation		Log-log

(GR9677 #27)

Solution:

(A) dN/dt ∝ e^−2t
log [dN/dt] ∝ log e^−2t
log [dN/dt] ∝ −2t
Activity vs time graph has a semilog plot.

(B) V_s ∝ f
Stopping potential vs frequency graph has a linear plot.

(C) s ∝ t²
log s ∝ 2 log t
Distance vs time graph has a log-log plot.

(D) V_out/V_in ∝ 1/ω
V_out/V_in ∝ ω⁻¹
log [V_out/V_in] ∝ − log ω
Gain vs frequency graph has a log-log plot, NOT linear.

(E) P ∝ T⁴
log P ∝ 4 log T
Power vs temperature graph has a log-log plot.

Answer: D

Notes:

A semilogarithmic graph has one axis in logarithmic scale and the other in linear scale.

A log-log graphs has both axes in logarithmic scale.