A 0.13-m string, fixed at both ends and vibrating in its n = 4 harmonic, excites a pipe that is $0.88 \mathrm {~m}$ 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

Quizplus · Accepted Answer

The string's fourth harmonic has a wavelength of $ \lambda = \frac{2L}{n} = \frac{2 \times 0.13}{4} = 0.065 \, \text{m} $. The pipe's second overtone is its third harmonic, with a wavelength of $ \lambda = \frac{2L}{3} = \frac{2 \times 0.88}{3} = 0.5867 \, \text{m} $. The frequency of the pipe's third harmonic is $ f = \frac{v}{\lambda} = \frac{345}{0.5867} \approx 588 \, \text{Hz} $. The string's frequency is the same, so $ v = f \lambda = 588 \times 0.065 \approx 38 \, \text{m/s} $.

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