A 0.13-m string,fixed at both ends and vibrating in its n = 4 harmonic,excites a pipe that is 0.88 m. Long and open at both ends,into its second overtone resonance.What is the speed of transverse waves on the string? The speed of sound in air is 345 m/s.
A)38 m/s
B)36 m/s
C)34 m/s
D)32 m/s
E)30 m/s

Question

A 0.13-m string,fixed at both ends and vibrating in its n = 4 harmonic,excites a pipe that is 0.88 m.  Long and open at both ends,into its second overtone resonance.What is the speed of transverse waves on the string? The speed of sound in air is 345 m/s.
A)38 m/s
B)36 m/s
C)34 m/s
D)32 m/s
E)30 m/s

Quizplus · Accepted Answer

- The fundamental frequency of a string fixed at both ends is given by f = (n/2L) * v, where n is the harmonic number, L is the length of the string, and v is the speed of transverse waves on the string.
- For the n = 4 harmonic, we have f = (4/2*0.13) * v = 15.38 v.
- The second overtone resonance of an open pipe is given by f = 3v/4L, where L is the length of the pipe and v is the speed of sound in air.
- For the second overtone resonance, we have f = 3v/4*0.88 = 1.03v.
- Equating these two frequencies gives 15.38 v = 1.03v, or v = 38 m/s.
- Therefore, the best choice is A) 38 m/s.

A 013-M String,fixed at Both Ends and Vibrating in Its N