14B beats - 4/15/2011 Clicker Question 14B-1 Physics 1C...

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4/15/2011 1 Physics 1C Lecture 14B "Shake this one, that one shakes later. The sun atom shakes; my eye electron shakes eight minutes later because of a direct interaction across." --Richard Feynman Clicker Question 14B-1 Two loudspeakers are in phase with each other. They emit sound waves of equal amplitude with a wavelength of 1.0 meter. At the point P indicated, the interference is: A) Completely constructive. B) Completely destructive. C) Something in between constructive and destructive. P Wave Interference Example Two strings with linear densities of 5.0g/m are stretched over pulleys, adjusted to have vibrating lengths of 50cm, and attached to hanging blocks. The block attached to string 1 has a mass of 20kg and the block attached to string 2 has mass M . Listeners hear a beat frequency of 2.0Hz when string 1 is excited at its fundamental frequency and string 2 at its third harmonic. What is one possible value for M ? Answer Here we need to make a diagram of the situation and list the known quantities. Wave Interference Answer Making a diagram we note that the mass creates the tension to increase the wave speed: Listing the quantities that we know: f beat = 2.0Hz L 1 = L 2 = 0.50m μ 1 = μ 2 = 5.0x10 -3 kg/m m 1 = 20kg Wave Interference Answer An observer hears a beat frequency of 2Hz so: The frequency for the first string will be: f beat 2Hz f 2 f 1 f n n v 2 L f 1 1   v 1 2 L 1 F T 1 2 L 1 f 1 m 1 g 1 2 L 1 Wave Interference Answer The frequency for the second string will be: f n n v 2 L f 2 3   v 2 2 L 2 3 F T 2 2 L 2 f 2 3
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14B beats - 4/15/2011 Clicker Question 14B-1 Physics 1C...

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