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$\bullet$ One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at 120 $\mathrm{Hz}$ . The other end passes over a pulley and supports a 1.50 $\mathrm{kg}$ mass. The linear mass density of the rope is 0.0550 $\mathrm{kg} / \mathrm{m}$ . (a) What is the speed of a transverse wave on the rope? (b) What is the wavelength?(c) How would your answers to parts (a) and (b) change if themass were increased to 3.00 $\mathrm{kg}$ ?
(a) $v_{1}=16.3 \mathrm{m} / \mathrm{s}$(b) $\lambda_{1}=0.136 \mathrm{m}$(c) $v_{2}=\sqrt{2} v_{1} \quad-\quad \lambda_{2}=\sqrt{2} \lambda_{1}$
Physics 101 Mechanics
Chapter 12
Mechanical Waves and Sound
Periodic Motion
Mechanical Waves
Sound and Hearing
Cornell University
Rutgers, The State University of New Jersey
Hope College
McMaster University
Lectures
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we're told that one end of the hose on a rope is attached to a prawn oven. Electrical electrically driven tuning for that vibrates what 20 hurt. The other end passes over a pulley and supports a 1.5 kilogram mass. The linear mass density. The rope is your point 055 kilograms per meter. And first we want to find what is the speed of a transfer Transfers wave in the rope. Look, here's our situation. We got here. We have a, uh I wrote attached to that was shaker here that's vibrating at 120 hertz. We have a mass attached to it that has a way of MT. And so we can figure out. Given our information here, you can figure out what the tension is, and then we can plug that in for our into our equation. Relating the tension, the mass density, the linear master speed looking that all in and we wind up with 16.3 meters per second. Well, then asked what is the wavelength? Well, given the frequency and the speed, we can calculate the weight of Lee and the wavelength is then, um, 13.6 centimeters we have then asked, How would your answers check your parts A and B changed if the mass were increased The three kilogram. Okay, so we can do our analysis Now we have a mass in prime of three kilograms, which is actually just twice our old mask. And if we look at the equation, we can see that our new, um that our new speed is going to be the square root of the mass racial times, old speed. So that is now a square to two times V, which is 23.1 meters per second. Likewise, the wavelength is the square root of the mass ratio times the old wavelength, So we get to a 0.19 meters are about 19 centimeters.
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