1 / 15

Waves at Boundaries

Waves at Boundaries. Waves at Boundaries. A wave transmits energy through a medium Eventually that wave will reach a boundary A boundary is an obstacle or even another medium that the wave reaches as it travels. Waves at Boundaries. What happens at the wave boundary?

Download Presentation

Waves at Boundaries

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Waves at Boundaries

  2. Waves at Boundaries • A wave transmits energy through a medium • Eventually that wave will reach a boundary • A boundary is an obstacle or even another medium that the wave reaches as it travels

  3. Waves at Boundaries • What happens at the wave boundary? • The initial wave travels at the boundary. This is the incident wave. • A portion of the energy flows into the new medium. This is called the transmitted wave. • A portion of the energy is reflected. This is called the reflected wave.

  4. Waves at boundaries • The incident wave and reflected wave can have 2 situations: • Fixed End • Free End • The transmitted wave depends on the density of the new medium

  5. Fixed end reflection • Fixed end reflection is when one end of the medium is attached to an object that cannot move • Think of a rope attached to a table Let’s talk about sending a wave pulse through this rope to help you visualize • The incident wave travels through the medium and hits the boundary • This will created a transmitted and wave and reflected wave • Let’s think about what will happen to the reflected wave…

  6. Fixed end reflection • The rope is pulling up at the fixed end. • For every reaction there is an equal and opposite reaction • The fixed end pulls down on the rope • The reflected wave comes back through the rope but has an inverted amplitude • The wavelength of the reflected wave is the same as the wavelength of the incident wave • The speed of the wave is still the same. Remember, speed depends on wavelength and frequency. These do not change. • The amplitude of the reflected wave is less than the amplitude of the incident wave • Remember, the amplitude squared of a mechanical wave is proportional to the energy of the wave. Some of the energy was sent to create a transmitted wave.

  7. Free end reflection • When the end of a medium is not attached and is free to move, we consider this the case of free-end reflection • Once again, let’s think about what happens when a wave pulse reaches the end of the rope • It will create a reflected and transmitted wave again.

  8. Free end reflection • The rope pulls up at the free end but nothing pulls down. • The reflected wave returns with but does not have an inverted amplitude • The wavelength remains the same for the reflected pulse • The speedof the wave remains the same • The amplitude is not inversed and is less than the incident wave

  9. Transmitted wave • No we will look at the transmitted wave at a boundary • The transmitted wave does not depend on free or fixed end • The transmitted wave depends only on the density of the medium for the incident wave and the density of the medium for the transmitted wave • The transmitted wave can be in either: • Higher density medium • Lower density medium

  10. High density medium for transmitted wave • We will examine what happens as a wave passes into a higher density medium from a lower density medium • As the wave reaches the boundary, some of the energy will continue into the new medium (transmitted wave) and some of the energy will be bounced back (reflected wave) • The reflected wave will: • Travel with a same speed as the incident wave • Have the same wavelengththan the incident wave • Have an inverted amplitudecompared to the incident wave • Frequency stays the same • The transmitted wave will: • Travel with a slower speed compared to the incident wave • Have a shorter wavelength than the incident wave • Amplitude is in the same direction as the incident wave • Frequency stays the same

  11. Lower Density Medium for Transmitted Wave • We will examine what happens as a wave passes into a lower density medium from a lower density medium • The reflected wave will: • Travel with a same speed as the incident wave • Have the same wavelengththan the incident wave • Amplitude is in the same direction as the incident wave • Frequency stays the same • The transmitted wave will: • Travel with a faster speedcompared to the incident wave • Have a longer wavelengththan the incident wave • Amplitude is in the same direction as the incident wave • Frequency stays the same

  12. Frequency, Velocity & Amplitude • Frequency • The frequency of the wave will be the same in both mediums. • Velocity • The velocity depends on the properties of each medium and therefore will be different in each medium. (less dense = faster, more dense = slower). • Amplitude • The amplitude is directly proportional to the velocity. (if v higher, amplitude is greater. If v is lower, amplitude is smaller)

  13. Calculations Involving Transmission of Waves • From the information we just went through, we should notice that the velocity and amplitude are proportional to each other when a wave changes mediums • If the new medium is less dense, the velocity and amplitude increase • If the new medium is more dense, the velocity and amplitude decrease • We also learned that frequency remains constant when a wave changes media • One thing we haven’t discussed yet is what happens to the wavelength when a wave changes media • Recall the “Universal Wave Equation”: v = fλ • If we know that the velocity will change in a new medium, then the wavelength must also change in a similar way in order for the relationship v = fλ to remain true.

  14. Calculations Involving Transmission of Waves • When solving a question where a wave changes mediums, remember that frequency is constant. Solve for it first, then use it to solve for whatever you need. • Example: A tow rope is connected to a slinky. A wave travelling at 1.50 m/s is introduced to the tow rope. After the wave is transmitted to the slinky, the wave is travelling at 5.35 m/s with a wavelength of 3.00 m. What is the initial wavelength of the wave in the tow rope? • You have enough info to solve for “f” in the slinky • v = fλ • f = v/λ • f = 5.35 m/s 3.00 m f = 1.78 Hz • Now, use that value of “f” to solve for the unknown wavelength • v = fλ • Λ = v/f • Λ = 1.50 m/s 1.78 Hz Λ = 0.843 m

  15. Calculations Involving Transmission of Waves • What we should also realize from this example is the following relationship: Vi= Vf λiλf • Where: • Vi = initial velocity • Λi = initial wavelength • Vf = final velocity • Λf = final wavelength • From the previous example • Vi = 5.35 m/s • Λi = 3.00 m • Vf = 1.50 m/s • Λf = ?

More Related