16.37 • Two small stereo speakers Figure E16.37 are driven in step by the same variable- frequency oscillator. Their sound is picked up by a microphone arranged as shown in Fig. E16.37. For what fre- quencies does their sound at the speak- ers produce (a) constructive interference and (b) destructive interference? 4.50 m- 2.00 m Microphone

16.37 • Two small stereo speakers Figure E16.37 are driven in step by the same variable- frequency oscillator. Their sound is picked up by a microphone arranged as shown in Fig. E16.37. For what fre- quencies does their sound at the speak- ers produce (a) constructive interference and (b) destructive interference? 4.50 m- 2.00 m Microphone

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter18: Superposition And Standing Waves

Section: Chapter Questions

Problem 10PQ

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Two identical loudspeakers 10.0 m apart are driven by the same oscillator with a frequency of f = 21.5 Hz (Fig. P17.6) in an area where the speed of sound is 344 m/s. (a) Show that a receiver at point A records a minimum in sound intensity from the two speakers. (b) If the receiver is moved in the plane of the speakers, show that the path it should take so that the intensity remains at a minimum is along the hyperbola 9x2 16y2 = 144 (shown in red-brown in Fig. P17.6). (c) Can the receiver remain at a minimum and move very far away from the two sources? If so, determine the limiting form of the path it must take. If not, explain how far it can go. Figure P17.6
In figure OQ18.1 (page 566), a sound wave of wave-lenght 0.8 m divides into two equal parts that recombine to interfere constructively, with the original difference between their path lengths being |r2 r1| = 0.8 m. Rank the following situations according to the intensity of sound at the receiver from the highest to the lowest. Assume the tube walls absorb no sound energy. Give equal ranks to situations in which the intensity is equal. (a) From its original position, the sliding section is moved out by 0.1 m. (b) Next it slides out an additional 0.1 m. (c) It slides out still another 0.1 m. (d) It slides out 0.1 m more.
On a marimba (Fig. P18.75), the wooden bar that sounds a tone when struck vibrates in a transverse standing wave having three ant modes and two nodes. The lowest-frequency note is 87.0 Hz, produced by a bar 40.0 cm long, (a) Find the speed of transverse waves on the bar. (b) A resonant pipe suspended vertically below the center of the bar enhances the loudness of the emitted sound. If the pipe is open at the top end only, what length of the pipe is required to resonate with the bar in part (a)?
(a) Echo times are measured by diagnostic ultrasound scanners to determine distances to re?ecting surfaces in a patient. What is the difference in echo times for tissues that are 3.50 and 3.60 cm beneath the surface? (This difference is the minimum resolving time for the scanner to see details as small as 0.100 cm, or 1.00 mm. Discrimination of smaller time differences is needed to see smaller details.) (b) Discuss whether the period T at this ultrasound must be smaller than the minimum time resolution. If so, what is the minimum frequency of the ultrasound and is that out of the normal range for diagnostic ultrasound?
(a) If a submarine’s sonar can measure echo times with a precision of 0.00100 s, what is the smallest difference in distances it can detect? (Assume that the submarine is in the ocean, not in fresh water.) (b) Discuss the limits this time resolution imposes on the ability of the sonar system to detect the size and Shape of the object creating the echo.
A bird-watcher is hoping to add the white-throated sparrow to her "life list" of species. How far could she be from the bird described in example 14-8 and still be able to hear it? Assume no reflections or absorption of the sparrow's sound. Express your answer using three significant figures in KM.
(II) The two sources of sound in Fig. 12–16 face each otherand 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(a) complete constructive interference occurs and (b) complete destructive interference occurs. (Assume ) T = 20°C.
(II) The two sources of sound in Fig. 12–16 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 (a) complete constructive interference occurs and (b) complete destructive interference occurs. (Assume ) T = 20°C
(II) A bug on the surface of a pond is observed to moveup and down a total vertical distance of 7.0 cm, from thelowest to the highest point, as a wave passes. If the ripplesdecrease to 4.5 cm, by what factor does the bug’s maximumKE change?
In Lake Michigan two completely identical sinusoidal waves superimpose. They have the same wave number (2.5m^-1), wave speed (500m/s), and amplitude (5cm). However, they are out of phase by 200°. What would be the resultants wave at x=3m and t=4s?
Two loudspeakers located along the x-axis as shown produce sounds of equal frequency. Speaker 1 is at the origin, while the location of speaker 2 can be varied by a remote control wielded by the listener. He notices maxima in the sound intensity when speaker 2 is located at x = 0.75 m and 1.00 m, but at no points in between. What is the frequency of the sound? Assume the speed of sound is 340 m/s.
Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 5.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 1.00 m parallel to the wall, she experiencesdestructive interference for the first time. What is the frequency of the sound? The speed of sound in air is 343 m/s.