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$\bullet$$\bullet$ Two identical audio speakers connected to the sameamplifier produce in-phase sound waves with a single fre-quency that can be varied between 300 and 600 Hz. The speedof sound is 340 $\mathrm{m} / \mathrm{s} .$ You find that where you are standing,you hear minimum-intensity sound. (a) Explain why you hearminimum-intensity sound. (b) If one of the speakers is moved39.8 $\mathrm{cm}$ toward you, the sound you hear has maximum inten-sity. What is the frequency of the sound? (c) How much closerto you from the position in part (b) must the speaker be movedto the next position where you hear maximum intensity?

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a) Hearing minimum intensity sound means the point where you are standing satisfies the conditionfor destructive interference $\Delta x=\left(m+\frac{1}{2}\right) \lambda .$ When destructive interference occurs, the intensity of the sound will be minimum.b) 427 Hzc) 0.796 m

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

Rutgers, The State University of New Jersey

University of Washington

McMaster University

Lectures

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

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So in this situation, we're going to get constructive interference whenever the distance between the two sources is equal to an inn is your number of wavelengths You're going get destructive interference when the distance between the two sources is 1/2 manager of the Wailea and some apart, eh? It's asking why we're getting deconstructive interference. And the answer is that the difference in distance between the sources must be 1/2 imager of the wailing. I'm not going to write that ox. I would take a lot time, but I just pretty much said the answer there to party. Barely qualitative for party. No part of it is quantitative, but part BNC is so in part B. We want to figure out what the frequency is given that if we move a certain distance away, we're now at a maximum. And so the path difference changed by Lando or two. Why do we know this? Well, it went from a D constructive interference to a constructive interference. And so the this has travelled for that to happen is half a wavelength, since the distance traveled for one constructive interference to another is a full wavelength. And so we know it must have traveled this distance and we know the distance to travel. It's just 3.398 meters and so we can solve this For Landa, you have a 0.796 meters and now we can use this famous identity. Frequency is speed over wavelength to solve for the frequency. And we get 427 hertz now and Parsi, we're moving to the next constructive interference. And so we're going to move another amount of the wavelength in order to get there. So we're going to move 0.796 away. Hey! And so the answer is actually just move one more labeling. So we're going to move points of the 96 meters, Yeah.

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