Two sounds with the same intensity occur at the same time and produce the interference pattern shown below. What two frequencies could plausibly produce this pattern? Explain your answer in terms of the beat frequency and the average frequency. N D (m) NLO 0 0.5 1.5 Time (s) O 14.5 Hz and 15.5 Hz 14 Hz and 16 Hz O 29 Hz and 30 Hz O 29 Hz and 31 HzThe sound of silence 1 point possible (graded) Two speakers, 51 and 52, in phase with each other produce sound waves that have the same frequency and sound intensity. They are separated by 4.0 In, as shown in the figure. Initially you are standing at point A, which is 3.0 m away from the halfway point between $1 and 32. s1 52 A 4-0m A 4" d} V V I 00 : is 20m E 3 no ----------- 6- ----- -o- ---------- c B A (a) Would you hear a maximum or a minimum in the sound level at point A? Explain your reasoning! (b) You then start moving to point B, which is directly in front of speaker 31. The sound level steadily decreases going from A to B, finally reaching a minimum exactly at point B. What is the wavelength of the sound generated by the speakers? (c) You now walk from B towards point C which is 20 m away from B as shown in the figure (the distance is not drawn to scale). Do you hear any maxima going from B to 0? Be very cautious with rounding and explain your reasoning. Stop interfering! 4 points possible (graded) You (a detective) have detected a potential case of interference of two travelling waves. A witness comes forward and presents you with some evidence - a snapshot graph of the resulting interference pattern taken at a time, t = 0 8 (shown below). A second witness informs you that both travelling waves were seen moving in the same direction, to the left, with a velocity of 2 m/s. A third witness confirms that one of the two travelling waves had a phase constant ($1) of 7r/2 and that the two travelling waves had the same amplitude and wavelength. 0 S) (m) D(x, t 1 o 0.5 1 1.5 2 2.5 3 Xim) (a) What are the wavelength and frequency of the two travelling waves that produced the interference pattern shown above? Hz (b) What is the phase constant of the second travelling wave (452) ? [Hintz How does the phase constant of the interference pattern of two waves travelling in the same direction depend on the phase constants of the original travelling waves?]. Note when reading values off the graph you can round to the nearest 0.1 111. Round your final answer to the nearest integer multiple of 7r/4. pi/4 (c) What is the amplitude of the two travelling waves that produced this interference? Round your answer to the nearest integer. Setting up your stereo 2 points possible (graded) Two speakers 31 and 82 are 10 m apart. The speakers emit sound of the same frequency and are in phase with each other. A person standing at point P hears a maximum (constructive interference) in sound level. 10m (a) What is the lowest possible frequency emitted by the speakers? Hz (b) What is the lowest possible frequency emitted by the speakers, if the two speakers are out of phase? Hz