Physics quiz question: comparing FM, AM radio wavelengths

Physics 205B Quiz 1, spring semester 2013
Cuesta College, San Luis Obispo, CA

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

"Under the radio towers on Capitol Hill"
Matthew Rutledge
flic.kr/p/5JTuuF

FM radio station KCBX broadcasts at 90.1 MHz, while AM radio station KVEC broadcasts at 920 kHz[*]. Radio signals from station __________ have a longer wavelength in air.
(A) KCBX.
(B) KVEC.
(C) (There is a tie.)
(D) (Not enough information given.)

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

Correct answer (highlight to unhide): (B)

Wave speed v depends on the properties of the medium. Frequency f depends on the properties of the source. These two parameters can be varied independently of each other.

The wavelength λ is the parameter dependent on both of the independent parameters:

λ = v/f.

Since the two radio waves have the same speed v (as they travel through the same medium), then because of their different frequencies, they will have have different λ wavelengths (as this parameter depends on both the wave source and the properties of the medium):

λ₁ = v₁/f₁,

λ₂ = v₂/f₂,

where v₁ = v₂ (as both waves travel through air). Because KCBX (here, station 1) has a much higher frequency than KVEC (here, station 2), then f₁ > f₂, and thus λ₁ < λ₂, and so KVEC broadcasts radio waves with the longer wavelength.

Section 30882
Exam code: quiz01b3Es
(A) : 16 students
(B) : 18 students
(C) : 1 student
(D) : 0 students

Success level: 54%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.45