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 4 antinodes, so its wavelength is $ \lambda = \frac{2 \times 0.13}{4} = 0.065 \, \text{m} $. The pipe's second overtone is its third harmonic, with a wavelength $ \lambda = \frac{2 \times 0.88}{3} = 0.5867 \, \text{m} $. The frequency is the same for both, so $ v_{\text{string}} = \frac{f \times 0.065}{f \times 0.5867} \times 345 = 38 \, \text{m/s} $.

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