The acoustical system shown in the figure below is driven by a speaker emitting sound of frequency 777 Hz. (Use v = 343 m/s.)A rectangular tube where the top section is comprised of a sliding U-shaped part has an opening at the center of the left and right sides of the tube. A speaker is pointed at the opening on the left side and shows sound waves entering the tube going through both paths towards the right opening. A human ear labeled Receiver is next to the right opening.(a) If constructive interference occurs at a particular instant, by what minimum amount should the path length in the upper U-shaped tube be increased so that destructive interference occurs instead? m(b) What minimum increase in the original length of the upper tube will again result in constructive interference? m
Question
The acoustical system shown in the figure below is driven by a speaker emitting sound of frequency 777 Hz. (Use v = 343 m/s.)A rectangular tube where the top section is comprised of a sliding U-shaped part has an opening at the center of the left and right sides of the tube. A speaker is pointed at the opening on the left side and shows sound waves entering the tube going through both paths towards the right opening. A human ear labeled Receiver is next to the right opening.(a) If constructive interference occurs at a particular instant, by what minimum amount should the path length in the upper U-shaped tube be increased so that destructive interference occurs instead? m(b) What minimum increase in the original length of the upper tube will again result in constructive interference? m
Solution
To solve this problem, we need to understand the concepts of constructive and destructive interference of waves.
(a) For destructive interference to occur, the path difference should be an odd multiple of half the wavelength. The wavelength (λ) can be calculated using the formula: λ = v/f, where v is the speed of sound (343 m/s) and f is the frequency (777 Hz).
First, calculate the wavelength: λ = 343 m/s / 777 Hz = 0.4417 m
Half of this wavelength is 0.4417 m / 2 = 0.2208 m.
So, the minimum amount the path length in the upper U-shaped tube should be increased by for destructive interference to occur is 0.2208 m.
(b) For constructive interference to occur again, the path difference should be an integer multiple of the wavelength. The minimum increase to achieve this would be one full wavelength, which we've already calculated as 0.4417 m.
So, the minimum increase in the original length of the upper tube to again result in constructive interference is 0.4417 m.
Similar Questions
A pair of speakers separated by distance d = 0.630 m are driven by the same oscillator at a frequency of 678 Hz. An observer originally positioned at one of the speakers begins to walk along a line perpendicular to the line joining the speakers as in the figure below. (Use v = 343 m/s.)Two speakers are side by side, with one speaker on the left and one on the right. The speakers are separated by a distance d and emit sound waves in the same direction. A man stands directly in front of the speaker on the right but a distance x away from the speaker.(a) How far must the observer walk before reaching a relative maximum in intensity? m(b) How far will the observer be from the speaker when the first relative minimum is detected in the intensity? m
Two speakers, facing each other, produce coherent sound waves that interfere destructively at a point that is ¾ of the way from one speaker to the other. If the speed of sound is 343 m/s, and the sound waves are emitted in phase at 880 Hz, which of the following is a possible distance between the two speakers?
Two loudspeakers are placed above and below each other, as in the figure below, and driven by the same source at a frequency of 5.20 ✕ 102 Hz. An observer is in front of the speakers (to the right) at point O, at the same distance from each speaker. What minimum vertical distance upward should the top speaker be moved to create destructive interference at point O? (Let h = 3.44 m and use v = 343 m/s.)Two speakers, one directly above the other, are separated by a distance h and point to the right. A horizontal line begins at the midpoint between the speakers and extends to the right. A point labeled O on the line is a distance 8.00 m to the right of the midpoint between the speakers. The distance from the top speaker to point O is labeled r1, and the distance from the bottom speaker to point O is labeled r2. An arrow points from each speaker to point O. Your response differs from the correct answer by more than 10%. Double check your calculations. m
Two omnidirectional 350 W loudspeakers are placed 10.0 m apart, each emitting a high- volume single tone in phase with each other, pitched at 261.63 Hz. (i) An observer is standing directly between the two speakers. Calculate the minimum distance that the observer should move towards one of the speakers to avoid hearing the sound emitted from the speakers
A pipe, closed at one end, has a loudspeaker at the open end. For some frequencies of soundfrom the loudspeaker, a stationary sound wave is formed in the air within the pipe with anantinode at the open end of the pipe.0.85 mloudspeaker pipeThe length of the pipe is 0.85 m.The speed of sound in air is 340 m s –1.Which frequency of sound from the loudspeaker would not produce a stationary wave?A 100 Hz B 200 Hz C 300 Hz D 500 Hz
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.