18. Waves & Sound

Wave Interference

Open Question
Two radio antennas A and B radiate in phase. Antenna B is 120 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied. (b) What is the longest wavelength for which there will be constructive interference at point Q?
Open Question
Two radio antennas A and B radiate in phase. Antenna B is 120 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied. (a) What is the longest wavelength for which there will be destructive interference at point Q?
Open Question
Two speakers that are 15.0 m apart produce in-phase sound waves of frequency 250.0 Hz in a room where the speed of sound is 340.0 m>s. A woman starts out at the midpoint between the two speakers. The room's walls and ceiling are covered with absorbers to eliminate reflections, and she listens with only one ear for best precision. (c) How far from the center must she walk before she first hears the sound maximally enhanced?
Open Question
Two speakers that are 15.0 m apart produce in-phase sound waves of frequency 250.0 Hz in a room where the speed of sound is 340.0 m>s. A woman starts out at the midpoint between the two speakers. The room's walls and ceiling are covered with absorbers to eliminate reflections, and she listens with only one ear for best precision. (a) What does she hear: constructive or destructive interference? Why?
Open Question
Two small stereo speakers A and B that are 1.40 m apart are sending out sound of wavelength 34 cm in all directions and all in phase. A person at point P starts out equidistant from both speakers and walks so that he is always 1.50 m from speaker B
(Fig. E35.1). For what values of x will the sound this person hears be (b) cancelled? Limit your solution to the cases where x … 1.50 m
Open Question
Two small stereo speakers A and B that are 1.40 m apart are sending out sound of wavelength 34 cm in all directions and all in phase. A person at point P starts out equidistant from both speakers and walks so that he is always 1.50 m from speaker B
(Fig. E35.1). For what values of x will the sound this person hears be (a) maximally reinforced. Limit your solution to the cases where x … 1.50 m
Open Question
"(II) Suppose two linear waves of equal amplitude and frequency have a phase difference ϕ as they travel in the same medium. They can be represented by ₁ ₂ ω θ
D₁ = A sin (kx - ωt)
D₂ = A sin ( kx - ωt + ϕ).
(d) Describe the resultant wave, by equation and in words, if ϕ = π/2 ."
Open Question
(II) The two sources of sound in Fig. 16–15 face each other and emit sounds of equal amplitude and equal frequency (305 Hz) but 180° out of phase. For what minimum separation of the two speakers will there be some point at which
(b) complete destructive interference occurs? (Assume T = 20°C .)
Open Question
(I) The two pulses shown in Fig. 15–37 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap.

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Open Question
(I) The two pulses shown in Fig. 15–37 are moving toward each other. (c) In Fig. 15–37, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

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Open Question
(II) Suppose two linear waves of equal amplitude and frequency have a phase difference ϕ as they travel in the same medium. They can be represented by ₁ ₂ ω θ
D₁ = A sin (kx - ωt)
D₂ = A sin ( kx - ωt + ϕ)
(b) What is the amplitude of this resultant wave? Is the wave purely sinusoidal, or not?