Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 23.7
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.
(C) (There is a tie.)
(D) (Not enough information given.)
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 difference 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.
Exam code: quiz01b3Es
(A) : 16 students
(B) : 18 students
(C) : 1 students
(D) : 0 students
Success level: 54%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.45