Practice Questions, Exam 1, Physics 102

Waves on Strings Two strings of different weights are glued together at their ends, and placed under 0.64 N of tension. The heavier string (m1 = 0.0004 kg/m) is on the right, and the lighter string (m2 = 0.0001 kg/m) on the left. A sinusoidal wave with frequency 63.66 Hz, is produced by shaking the heavy end of the two-part string. This wave starts at a peak, and has amplitude 10mm. For this problem, use coordinates where rightward is the +x direction, and leftward is the x direction. Find the speed of an elastic wave travelling on each of these strings. Which of the following displacement functions represents the original wave? a) 10cos(10x - 400t) b) 10cos(10x + 400t) c) 10cos(10x + 800t) d) 7cos(10x - 400t) e) 4cos(5x + 400t) f) 10cos(10x - 400t + p) Which of the following displacement functions represents the transmitted wave, which moves on to the lighter string? a) 10cos(5x + 400t) b) 7cos(5x - 400t) c) 4cos(10x + 800t) d) 10cos(10x + 400t) e) 4cos(5x + 400t) f) 7cos(10x - 400t) Which of the following displacement functions represents the reflected wave? a) 7cos(10x - 400t) b) 10cos(5x - 400t) c) 7cos(10x - 400t + p) d) 7cos(10x + 800t) e) 4cos(10x - 800t) f) 4cos(5x + 400t + p) Rewrite the displacement function for the original wave as it would appear if the wave started with a zero, rather than a peak.

Interference In order to check the spacing between two gears in a miniature motor, you shine a green laser light with wavelength 530 nm through the gap between them. a) Measuring the diffraction pattern, you determine that the central maximum is 0.12 radians wide. What is the width of the gap between the gears? b) Its generally easier to measure larger distances. Will you get more accurate results for gap spacing if this experiment is done under water? Why/why not? c) Will you get more accurate results for gap spacing if this experiment is done using red laser light instead? Why/why not? Standing Wave A guitar string has a length of 0.68m and a mass of 0.003kg. a) What tension must be applied to this string for it to vibrate at a frequency of 261.5Hz (middle C) when plucked? b) Pressing down on the string shortens the length thats free to vibrate. How far from the end of the string should you press down, if you want it to vibrate at 330Hz (E above middle C)?