Problem 3. Two stationary speakers (call them speaker I and speaker 2) are a distance (I = 2m apart. The sound produced is 335(le and both speakers have an average power of 400\"\". Assume air temperature is 20C. Alice stands equidistant from each speaker but a perpendicular distance :r: = 2{}m to the right. a) Suppose the speakers have the same initial phase, on. but. speaker I is turned on 2.0015 before speaker 2. What kind of interference will Alice observe? bu) Again suppose speaker I is turned on first, this time [8.1915 before speaker 2. Additionally, the bottom speaker begisz with a different initial phase. (:31. If Alice observes constructive interference at her location. what is the initial phase difference, 951 as = 1399'? C) Now suppose both speakers are turned on at the same time with the same initial phase. Alice walks parallel the two speakers from her initial location. How far must Alice walk until she observes destructive interference for the second time? (1) Someone changes the speaker settings and there is a new but unknown frequency. In addition. speaker 2 begins a quarter cycle ahead of speaker 1. Alice goes back to her initial location and again walks parallel the two speakers. Alice hears destructive interference after walking 5m. vill-That is the new 'equency? e) If the waves constructively interfere at Alice's initial location. what sound level will she hear? Bob shows up and hears lUdB while standing directly to the right of Alice. How far is he from Alice? Problem 4. A string of length 2m with both ends fixed is plucked by some curious students. The observe two different standing waves. the first with 6 nodes. and the second with 4 nodes. The frequency of the rst is 15(1H 2: higher than the second. a) W'hich harmonics are the two standing WHVBS? b) What is the wavelength of the first harmonic? c) W'hat is the speed of the waves on the string? (1) What is the frequency of the harmonic between the two you created? e) You want to use this string as part of a musical instrument. What frequency would you hear from the fundamental produced on this string? f) If one of the ends is made free rather than fixed, what is the frequency of the first harmonic? Problem 5. Bob is on a train traveling at 80m/s. His friend Alice is on a train platform as Bob approaches. Bob sends continuous signal in the form of a 1H z sound wave. a) What frequency will Alice measure as Bob approaches the platform? b) As Bob passes by and moves away from the platform, what frequency does Alice now measure? c) As Bob moves away from the platform, some of the sound waves bounce off the platform and return to him. What frequency does Bob measure for the returning signal? d) Another train is traveling next to Bob but moving more slowly at constant speed. Some of the sound reflects off of the other train and returns to Bob in the form of a 0.68/H z signal. How fast is the other train moving