Docs the transmitted wave has the same phase or not? [ See part B.] D. Imagine y

Question

Docs the transmitted wave has the same phase or not? [ See part B.] D. Imagine you have a rope with one end tied to a pole. Now you hold onto the other end of the rope and try to shake the rope. Now answer the following questions: Consider two ropes of equal length. One rope has more density compared to the other one. Which rope is easy to shake? Based on the above analogy which one is eloser to the "fixed end" scenario in the simulation in part A? Select the correct answer and explain. [ The disturbance is in a sense trying to shake the second rope into which it is trying to move in' If we make the second rope infinitely dense (thus infinitely heavy) will the disturbance be able to move the second rope?] When a wave travels from a lighter rope to a denser rope When a wave travels from a denser rope to a lighter rope Which one is closer to the "loose end" scenario in the simulation in part A? Select the correct answer and explain. When a wave travels from a lighter rope to a denser rope When a wave travels from a denser rope to a lighter rope Under what conditions docs the incident and reflected w ave Have the same phase? Have opposite phases?

Explanation / Answer

C)

The reflection of sound follows the law "angle of incidence equals angle of reflection", sometimes called the law of reflection. The same behavior is observed with light and other waves, and by the bounce of a billiard ball off the bank of a table. The reflected waves can interfere with incident waves, producing patterns of constructive and destructive interference. This can lead to resonances called standing waves

The phase of the reflected sound waves from hard surfaces and the reflection of string waves from their ends determines whether the interference of the reflected and incident waves will be constructive or destructive. For string waves at the ends of strings there is a reversal ofphase and it plays an important role in producing resonance in strings. Since the reflected wave and the incident wave add to each other while moving in opposite directions, the appearance of propagation is lost and the resulting vibration is called a standing wave.

2b)

Consider a thick rope attached to a thin rope, with the incident pulse originating in the thick rope.

There will be partial reflection and partial transmission at the boundary.

Since the incident pulse is in a heavier medium, when it reaches the boundary, the first particle of the less dense medium does not have sufficient mass to overpower the last particle of the more dense medium. The result is that an upward displaced pulse incident towards the boundary will reflect as an upward displaced pulse

Consider a thick rope attached to a thin rope, with the incident pulse originating in the thick rope

The transmitted pulse (in the less dense medium) is traveling faster than the reflected pulse (in the more dense medium

Waves always travel fastest in the least dense medium.

The transmitted pulse (in the less dense medium) has a larger wavelength than the reflected pulse (in the more dense medium

Particles in the more dense medium will be vibrating with the same frequency as particles in the less dense medium. Since the transmitted pulse was introduced into the less dense medium by the vibrations of particles in the more dense medium, they must be vibrating at the same frequency. So the reflected and transmitted pulses have the different speeds but the same frequency. Since the wavelength of a wave depends upon the frequency and the speed, the wave with the greatest speed must also have the greatest wavelength.
•   The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse.

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