Physics quiz question: guitar string wave speed

Physics 205A Quiz 6, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 11.9

A metal guitar string has a linear mass density of 3.6 g/m, and is stretched with a tension of 130 N. The speed of transverse waves on this string is:
(A) 5.3×10^–3 m/s.
(B) 0.68 m/s.
(C) 190 m/s.
(D) 3.6×10⁴ m/s.

Correct answer (highlight to unhide): (C)

The speed of transverse waves along this string is:

v = √(F/(m/L)),

where F is the tension in the string, and (m/L) is the linear mass density (mass per unit length) of the string. Plugging in the given values, where (m/L) must be properly given in units of kg/m:

v = √((130 N)/(0.0036 kg/m)) = 190.0292375 m/s,

or to two significant figures, v = 1.9×10² m/s.

(Response (A) is √((m/L)/F); response (B) is sqrt(F·(m/L)); and response (D) is F/(m/L).)

Student responses
Sections 30880, 30881
(A) : 5 students
(B) : 1 student
(C) : 28 students
(D) : 6 students

Success level: 70%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.62