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Chapter 35: Problem 58

The professor returns the apparatus to the original setting. She then adjusts the speakers again. All of the students who had heard nothing originally now hear a loud tone, while you and the others who had originally heard the loud tone hear nothing. What did the professor do? (a) She turned off the oscillator. (b) She turned down the volume of the speakers. (c) She changed the phase relationship of the speakers. (d) She disconnected one speaker.

Short Answer

Expert verified
The professor changed the phase relationship of the speakers. (c)

Step by step solution

01

Understanding Sound Interference

Sound waves from two speakers can interfere giving rise to constructive interference (loud sound) and destructive interference (no sound). Constructive interference happens when the two speakers are at the same phase - the loud sounds heard at some regions. Destructive interference happens when the two speakers are at opposite phase - silence is heard at some regions.
02

Identify the change

The professor changed the setup so that the students who were originally in the region of constructive interference now are in the region of destructive interference, and vice versa. This change can't be brought about by turning off the oscillator or turning down the volume of the speakers or disconnecting one speaker. Thus, the professor must have changed the phase relationship of the speakers. This implies she shifted the phases of the sound waves such that those who were initially in constructive interference regions are now in the destructive ones and vice versa.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Constructive Interference
When two sound waves meet and combine to create a louder sound, this is known as constructive interference. It occurs when waves from different sources arrive at the same point in such a way that their crests and troughs align. The sound waves add together, resulting in a wave with a higher amplitude.

Think of it as two waves high-fiving: if both waves 'hands' are up (crests) or down (troughs) at the same time, they add up to a bigger high five (louder sound). This is the case of being 'in phase', meaning the peaks and valleys of the waves occur at the same time and place. In the classroom scenario, the professor initially set the speakers so that their sound waves combined constructively at certain points, where students heard a loud tone.
Destructive Interference
Destructive interference occurs when two sound waves meet and cancel each other out, resulting in a reduction in volume or complete silence. This happens when the crest of one wave meets the trough of another wave.

Using our previous analogy, imagine one wave's hand is up (crest) while the other wave's hand is down (trough) 鈥� instead of a high five, they miss each other, leading to no sound (silence). More technically, the waves are 'out of phase', meaning the peaks of one wave correspond to the valleys of the other and they negate each other. When the professor adjusted the speakers again, the phase relationship was altered so that the students initially hearing sound now heard silence 鈥� a classic example of destructive interference.
Phase Relationship
The phase relationship between two waves describes how the peaks and troughs of the waves align with each other over time. If the peaks of one wave align with the peaks of another, they are said to be 'in phase'. But if the peaks of one wave align with the troughs of the other, they are 'out of phase'. The latter scenario leads to destructive interference, while the former leads to constructive interference.

The alteration of this relationship is what allows sound engineers, and in this case, the professor, to manipulate sound. By changing the phase relationship, as the professor did, you can change the areas of constructive and destructive interference in a room. This is a basic principle used in various applications, from noise cancellation headphones to acoustic engineering in concert halls.

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Most popular questions from this chapter

Coherent light with wavelength \(600 \mathrm{nm}\) passes through two very narrow slits and the interference pattern is observed on a screen \(3.00 \mathrm{~m}\) from the slits. The first-order bright fringe is at \(4.84 \mathrm{~mm}\) from the center of the central bright fringe. For what wavelength of light will the first-order dark fringe be observed at this same point on the screen?

Laser light of wavelength \(510 \mathrm{nm}\) is traveling in air and shines the at normal incidence onto the flat end of a transparent plastic rod that has \(n=1.30 .\) The end of the rod has a thin coating of a transparent material that has refractive index \(1.65 .\) What is the minimum (nonzero) thickness of the coating (a) for which there is maximum transmission of the light into the rod; (b) for which transmission into the rod is minimized?

Two light sources can be adjusted to emit monochromatic light of any visible wavelength. The two sources are coherent, \(2.04 \mu \mathrm{m}\) apart, and in line with an observer, so that one source is \(2.04 \mu \mathrm{m}\) farther from the observer than the other. (a) For what visible wavelengths \((380\) to \(750 \mathrm{nm})\) will the observer see the brightest light, owing to constructive interference? (b) How would your answers to part (a) be affected if the two sources were not in line with the observer, but were still arranged so that one source is \(2.04 \mu \mathrm{m}\) farther away from the observer than the other? (c) For what visible wavelengths will there be destructive interference at the location of the observer?

Two thin parallel slits that are \(0.0116 \mathrm{~mm}\) apart are illuminated by a laser beam of wavelength \(585 \mathrm{nm}\). (a) On a very large distant screen, what is the total number of bright fringes (those indicating complete constructive interference), including the central fringe and those on both sides of it? Solve this problem without calculating all the angles! (Hint: What is the largest that \(\sin \theta\) can be? What does this tell you is the largest value of \(m ?\) (b) At what angle, relative to the original direction of the beam, will the fringe that is most distant from the central bright fringe occur?

Two radio antennas \(A\) and \(B\) radiate in phase. Antenna \(B\) is \(120 \mathrm{~m}\) to the right of antenna \(A .\) Consider point \(Q\) along the extension of the line connecting the antennas, a horizontal distance of \(40 \mathrm{~m}\) 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 \(Q ?\) (b) What is the longest wavelength for which there will be constructive interference at point \(Q ?\)
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