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. What is the speed of transverse waves on this string?

(A) 5.3×10

^{–3}m/s.

(B) 0.68 m/s.

(C) 190 m/s.

(D) 3.6×10

^{4}m/s.

Correct answer (highlight to unhide): (C)

For transverse waves on a string, the wave speed is given by:

*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*= 1.9×10

^{2}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