Physics 7 E Prof D Casper Vibrations in

Physics 7 E Prof. D. Casper

Vibrations in Time and Space • • A wave satisfies both sets of equations – it is a moving disturbance with time AND space derivatives.

The Wave Equation •

Solutions to the Wave Equation •

Wave Speed on a Rope • Force, meaning tension in rope or spring (N) mass per unit length (kg/m)

Q 15. 8 The four strings of a musical instrument are all made of the same material and are under the same tension, but have different thicknesses. Waves travel A. fastest on the thickest string. B. fastest on the thinnest string. C. at the same speed on all strings. D. not enough information given to decide

A 15. 8 The four strings of a musical instrument are all made of the same material and are under the same tension, but have different thicknesses. Waves travel A. fastest on the thickest string. B. fastest on the thinnest string. C. at the same speed on all strings. D. not enough information given to decide

Comparing Speeds Two identical strings are held • under different tensions. Waves are measured to travel at 10. 0 m/s on the first string, and 40. 0 m/s on the second string.

Rock Climbing A rock-climber (60 kg) hangs from a rock climbing rope with a density of 0. 05 kg/m. If she jerks the rope to signal her partner 40 m above, how fast does the wave travel?

Hanging Rope A climbing rope with a density of 0. 05 kg/m hangs 70 m long. At the rope’s midpoint, what is the speed of traveling waves? A) 6 m/s B) 11 m/s C) 19 m/s D) 26 m/s E) 38 m/s

Don’t Confuse Speeds! • •

Boundaries A wave passes from one medium • into a second, denser medium (e. g. from a thin rope into a thick one, from air into water, etc)

Challenge Problem A climbing rope with a density of 0. 05 kg/m hangs 70 m long. How much time is required for a wave to travel from one end to the other?