Physics quiz question: linear mass density of viola string

Physics 205A Quiz 6, fall semester 2019
Cuesta College, San Luis Obispo, CA

Transverse waves travel at a speed of 357 m/s along a viola's A-string, stretched to a tension of 52.9 N[*][**]. The linear mass density of this string is:
(A) 4.15×10^–4 kg/m.
(B) 2.20×10^–2 kg/m.
(C) 0.148 kg/m.
(D) 0.385 kg/m.

[*] theviolaworkshop.com/page16.html.
[**] gamutmusic.com/viola-tensions.

Correct answer (highlight to unhide): (A)

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

v = √(F/(m/L)).

Solving for the linear mass density results in:

v² = F/(m/L),

(m/L) = F/(v²),

(m/L) = (52.9 N)/(357 m/s)² = 0.000415067988 kg/m,

or to three significant figures, 4.15×10^–4 kg/m.

(Response (B) is (F/v)²; response (C) is F/v; response (D) is √(F/v).)

Sections 70854, 70855
Exam code: quiz06co6O
(A) : 35 students
(B) : 7 students
(C) : 8 students
(D) : 2 students

Success level: 67%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.78