Question1

A pipe open only at one end has an essential frequency of 269 Hz. A second pipe, initially identical to the first pipe, is shortened by cutting off a portion of the open end. Now, as both pipes vibrate at their fundamental frequencies, a beat frequency of 13.2 Hz is heard. How many centimeters were cut off the end of the second pipe? The speed of sound is 343 m/s.

Question2

A particle travels horizontally between two parallel walls detached by 18.4 m. It moves toward the opposing wall at a constant rate of 8.3 m/s. In addition, it has acceleration in the direction parallel to the walls of 4.8 m/s. At what angle with the wall will the particle strike?

Question3

A drunken sailor stumbles 415 meters north, 365 meters northeast, and then 315 meters northwest. What are the total displacement and angle of the displacement? (Imagine east is the +x-direction and north is the +y-direction.)