Physics quiz question: making wavelength increase?

Physics 205A Quiz 6, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e Multiple-Choice Questions 11.5, 11.6

A steel cable 10.0 m long is pulled by a certain amount of tension. __________ of the steel cable would increase the wavelength of waves along the steel cable.
(A) Using a longer length.
(B) Decreasing the tension.
(C) (Either of the above choices.)
(D) (Neither of the above choices.)

Correct answer (highlight to unhide): (D)

The speed v of transverse waves along strings depends on the tension F and the linear mass density (mass per unit length) (m/L):

v = √(F/(m/L)).

Also the wavelength λ is the parameter that depends on the speed v and source frequency f, which can be varied independently of each other:

λ = v/f.

Using a longer length of this steel cable (with all other parameters fixed) would not affect the speed; while the length would get longer, the mass would proportionally increase as well, leaving the ratio (m/L) = (mass/length) unchanged.

Decreasing the tension F of the steel cable would decrease the speed v, and this would decrease the wavelength λ. Thus neither using a longer length of steel cable nor decreasing the tension of the steel cable would result in increasing the wavelength.

Sections 70854, 70855, 73320
Exam code: quiz06wR3k
(A) : 22 students
(B) : 27 students
(C) : 5 students
(D) : 9 students

Success level: 14%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.23