A piano consists of 88 keys each of which strikes one or more strings (though most keys have three strings). For the moment, assume that all of the strings have the same wave speed. The highest note on the piano has a frequency 4200 Hz, while the lowest note has a frequency 30 Hz. a.) Find the ratio of the lengths of the longest and shortest strings in the piano.
b.) If you open up a piano and measure the length of the shortest string, it is about 5 cm. If all strings have the same wave speed, what would the length of the longest string have to be?
c.) Based on your results, do you think all piano strings have the same wave speed? Explain.

Initially, a particle is moving at 5.33 m/s at an angle of 37.9° above the horizontal. two seconds later, its velocity is 6.11 m/s at an angle of 54.2° below the horizontal. what was the particle's average acceleration during these 2.00 seconds in the x-direction (enter first) and the y-direction?

1. a net force of 100 newton’s is applied to a wagon for 5 seconds. this causes the wagon to undergo a change in momentum of

5submission this assignment is worth 20 points total. you are required to submit the following by next lab: 1. (3 points) determine the equation for the output angular velocity ω2 = θ˙ 2 as a function of θ1, ω1 = θ˙ 1 and α. you must show all your work to receive credit. 2. (2 points) use the result of problem#1 to plot ω2 over 0 ≤ θ1 ≤ 360deg with ω1 = 360deg/sec. do this for α = {10,30}deg. show the results on the same plot and properly label the axes, title, legend. for this you can use matlab or ms excel. 3. (3 points) determine the equation for the output angular acceleration ω˙ 2 and create a plot similar to the one in problem#2. 4. (10 points) submit plots of the results (ω2 and ω˙ 2) obtained from creo/mechanism and compare them to results of problem#2 and problem#3. note that you should do these comparisons for the two cases with α = {10,30}deg. 5. (2 points) provide a brief explanation of the results. did they match? what are the implications as misalignment angle increases?