Question

question 4-7

4. Travelling Waves and Their Characteristics A rope wave travels in the positive x -direction. You are also told that the speed of the wave is 1000 cm/s, its frequency is 200 Hz, and that the wave is subject to the following initial conditions: at x 0 and t = 0: y =-1 cm, and, at x = 0 and t : ar = +20 cm/s (this is the velocity of the point on the rope at horizontal location zero in the vertical direction at time zero). Determine the vertical acceleration of the point on the string at x 2 cm for time t-2s 5. Electric Force, Electric Field, Superposition, Discrete Charges See Figure 1. Two point charges are stationary and arranged as shown. Charge q+5pC, charge q2 =-2 prC, and the distance that separates the point charges is 1 = 10 cm. 10 kg is placed directly above q2 at point P +3C and mass m a) If a charge of qs which is at a height h = 24 cm, what is the acceleration of the particle at this point? Give in unit-vector notation. With the situation as described for (a), if we do away with charge q, so that we only have b) charges qs and q2 a fixed distance l apart, where along a line passing through both g, a qz will the electric field be 0, besides infinitely far away? 6. Electric Force, Uniform Electric Field, Newton's Lows A bob is charged and attached to the end of an insulating, massless thread. To begin with, the string with the bob at the end hang vertically. A uniform electric field, due to a single charged sheet, is then turned on, and it points to the left. See Figure 2. The string will deviate from the vertical by a total amount of 30 until the bob comes to a halt and remains suspended in +10AC, and the ar equillbrium. The mass of the bob is 10 grams, its charge is q charged sheet is 5 cm2. You can set g 10 m/s a) Find the tension along the string b) Find the magnitude of the total charge on the sheet. 7. Electric Field, Superposition, Continuous Charge Distribution See Figure 3. An arc of total static charge -2Q (Q 0) covers the third quadrant. The radial distance from the arc to point P, at the origin, is R. Another arc of total static charge +40 spans the entire first quadrant, and it is of radius 4R from point P. What is the magnitude and direction of the net electric field at point P? Give magnitude in terms of the given quantities Q, R, and Eo Assume that the charge across each arc is uniformly distributed. Do 6 of 7 problems. Anything extra will be counted towards extra credit (up to 10 points). 1. Sound Intensity, Sound Level A point source of sound emits sound waves uniformly in 3D space (or, isotropically) at a constant rate of 100 watts. At a certain radial distance away from the point source, you are told that the sound level is 130 dB. What is the radial distance? a) In a time span of 10 seconds, how much sound energy is intercepted an area of 5 cm2 at the same radial distance. b) 2. Doppler Effect A bat glides along the positive x -axis at a uniform velocity of 15.0 m/s while a rodent, which is initially to the right of the bat by a fair distance, runs along in the opposite direction (towards the bat) at a uniform velocity of 5.00 m/s. The bat emits a sound wave at a frequency of 30 x 10 Hz. The wave will strike the rodent and perfectly reflect back towards the bat. What is the frequency of this echo as detected by the bat? Take the speed of sound to be 343 m/s. 3. Standing Waves A guitar string is clamped at both ends and is under a certain tension as it lies horizontally (along the x - axis, say). When plucked, the vibrating string is found to have a harmonic at a frequency of 2500 Hz. When plucked another way, the vibrating string is observed to have a harmonic at a frequency of 3500 Hz. You are told these harmonics are consecutive odd modes of oscillation. The velocity of the travelling waves is 100 m/s. Determine the length of the string. a) If the length of the string were tripled and the mass of the string increased by a factor of 9 (that is, 9 times as much as originally), with all else the same, how would the frequency b) (for any harmonic) change?

Answer 1

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