Physics quiz question: wavelength of changed frequency radio station

Physics 205B Quiz 1, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 23.7

FM radio station KCPR broadcasts at 91.3 MHz. The closest unused FM frequency for this area[*] is at 91.9 MHz. If KCPR were instead to broadcast at 91.9 MHz, its wavelength would be __________ compared to broadcasting at 91.3 MHz.
(A) shorter than.
(B) the same as.
(C) longer than.
(D) (Not enough information given.)

[*] radio-locator.com/cgi-bin/vacant?select=city&city=San%20Luis%20Obispo&state=CA.

Correct answer (highlight to unhide): (A)

Wavelength λ depends on both the speed v and frequency f:

λ = v/f.

Since the speed of radio waves depends only on the medium (air), and is independent of changes in frequency (ignoring negligible dispersion effects), an increase in frequency would result in a decrease in wavelength.

Sections 30882, 30883
Exam code: quiz01ksB4
(A) : 30 students
(B) : 3 students
(C) : 7 students
(D) : 0 students
(No response) : 1 student

Success level: 73%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.70