A 20m long rope bridge has a linear density of 4.8kg/m and is pulled to a tensio

Question

A 20m long rope bridge has a linear density of 4.8kg/m and is pulled to a tension of 25m.
A) What's the wave speed on this bridge?
B) What is the fundamental frequency?
C) What standing harmonic wave most closely matches a typical footstep frequency of 1.25Hz?
A 20m long rope bridge has a linear density of 4.8kg/m and is pulled to a tension of 25m.
A) What's the wave speed on this bridge?
B) What is the fundamental frequency?
C) What standing harmonic wave most closely matches a typical footstep frequency of 1.25Hz?

A) What's the wave speed on this bridge?
B) What is the fundamental frequency?
C) What standing harmonic wave most closely matches a typical footstep frequency of 1.25Hz?

Explanation / Answer

Answer:

(a) speed of the wave v = (T/linear density)1/2

v = (25/4.8 x 10-3)1/2 = 72.16 m/s

(b) Fundamental frequency = v/ 2L = 72.16/40 = 1.80 Htz

(c) All harmonics would be multiple of of this fudamental frequency. So foot step frequecy of 1.25 hrtz would be close to fundamental frequency.

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