Exhibit 16-3
Four wave functions are given below.
I.y(x, t) = 5sin(4x - 20t + 4)
II.y(x, t) = 5sin(3x - 12t + 5)
III.y(x, t) = 5cos(4x + 24t + 6)
IV.y(x, t) = 14cos(2x - 8t + 3)
Use this exhibit to answer the following question(s).
-Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wavelengths, from least to greatest.
A) IV, II, I, III
B) IV, I, II, III
C) I, II, III, IV
D) IV, II, III = I
E) I = III, II, IV

Question

Quizplus · Accepted Answer

The wavelength ($\lambda$) of a wave is inversely proportional to the coefficient of $x$ in the wave function, given by the general form $y(x, t) = A\sin(kx - \omega t + \phi)$ or $y(x, t) = A\cos(kx - \omega t + \phi)$, where $k = 2\pi/\lambda$. For the given wave functions, the coefficients of $x$ are 4 for I and III, 3 for II, and 2 for IV. Thus, the order from least to greatest wavelength is I = III (same $k$, so same $\lambda$), II, and IV.

Exhibit 16-3 Four Wave Functions Are Given Below