Part B 1. (a) A light source shines through two slits. The light has wavelength 450 nm, and the slits are 15 um apart. The pattern from the slit is projected onto a screen 0.15 m away, and the separation of the fringes is measured on the screen. What is the measured separation in metres? (5) (b) Two loudspeakers (set up in phase with each other) are located at two adjacent corners (A and B) of a square ABCD. Standing at the midpoint of side CD, you can hear a loud sound. As you walk from the midpoint to corner C, you hear the sound get much quieter, and then louder again as you get to C. If you keep walking, the sound starts to get quieter again. If the length of each side of the square is 4.4 m, find the frequency of the sound coming from the loudspeakers. (10) (take the speed of sound to be 343 ms-1) 2. A plate is dropped vertically on the floor and smashes into 3 pieces. The pieces fly apart horizontally. (a) What is the horizontal momentum of the plate just before it smashes apart? (1) (b) The 3 fragments fly apart as follows: . first fragment: mass my, velocity 3.00 ms" at an angle of 15.0' west of north; . second fragment: mass my, velocity 1.10ms" at an angle of 45.0' north of east; . third fragment: mass 0.130 kg, velocity 3.07 ms_ due south. Find the masses my and my- (10) (c) Calculate the total kinetic energy of the fragments, and hence the height from which the plate was dropped. (4) 3. 25.0m of copper wire is used to make a solenoid, by wrapping it around a cylinder. The solenoid is connected to a 3.00 V battery and the magnetic field inside the solenoid is found to be 6.48 x 10 3 T. (a) The wire is tightly wrapped, so that there is no space between the loops. Show that the number of turns per unit length of the solenoid is given by N T 2r where r is the radius of the cross-section of the wire. (3) (b) Find the radius of the cross-section of the wire. (12) (You can ignore the thickness of the insulation of the wire. The resistivity of copper is 1.68 x 10 (m.)4. 0.7 mole of an ideal gas is taken from state A (the left-hand point on the PV-plot below) to state PTIO'S Paj 0.0130 B (the middle point) and then state C (the right-hand point). (a) Calculate the final temperature of the gas (3) (b) Calculate the work done on (or by) the gas as it moves from state A to state C. (4) (c) i. Does heat leave or enter the system during this process? (2) ii. How much heat leaves or enters? (2) Explain why. (2) iv. Do you have to assume that the ideal gas is monatomic to get these results? Explain why. (2)