Reflection of Waves on a String: Understanding Mass and Phase Differences"

In summary, When sending a pulse down a string with mass (m1) and encountering a point where the mass of the string becomes (m2), two scenarios can occur: (i) if m1 is greater than m2, the wave is reflected with the same phase as the incident wave, and (ii) if m1 is less than m2, the wave is reflected 180 degrees out of phase with the incident wave. This is an experimental fact and can be explained theoretically through the Fresnel equations. Additionally, it is mathematically shown that if m2 is infinitely larger than m1, the amplitude of the reflected wave is equal to the incident wave. However, this may seem physically inconsistent as one would expect the
  • #1
Aequiveri
15
0
If I send a pulse down a string with mass (m1), consider what happens at a point where the mass of the string becomes (m2):

i) If m1 > m2, the wave is reflected with the same phase as the incident wave.
ii) If m1 < m2, the wave is reflected 180 degrees out of phase with the incident wave.

(Let's ignore any transmitted wave)

Why is this so? Is it an experimental fact, or is there some kind of theoretical/mathematical explanation for this behavior.

And I can see mathematically why it is the case that if m2 is infinitely larger than m1 (i.e. no transmitted wave - the end of the string is nailed down) the amplitude of the reflected wave is equal to the incident wave, but this seems physically inconsistent to me; if (ii) is true, shouldn't the reflected wave be equal to the "negative" amplitude of the incident wave?

I appreciate any insight you can give me. Thanks!
 
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  • #2
Perhaps the Fresnel equations provide the necessary theoretical explanation?
 
  • #3
Aequiveri said:
the amplitude of the reflected wave is equal to the incident wave, but this seems physically inconsistent to me; if (ii) is true, shouldn't the reflected wave be equal to the "negative" amplitude of the incident wave?

I think the incident and reflected wave amplitudes ARE opposite; isn't the result a standing wave on the incident wave side of the barrier?
 

1. What is the concept of wave reflection on a string?

The concept of wave reflection on a string refers to the behavior of waves when they encounter a boundary or obstacle on a string. When a wave reaches the end of a string, it is partially reflected back and partially transmitted. The reflected wave travels in the opposite direction with the same speed and amplitude as the incident wave, but with a phase difference of 180 degrees.

2. How does the mass of a string affect wave reflection?

The mass of a string affects wave reflection by influencing the speed of the wave. A heavier string will result in a slower wave speed, leading to a longer wavelength and lower frequency. This change in wavelength and frequency affects the phase difference between the incident and reflected waves, resulting in a change in the intensity of the reflected wave.

3. What role does phase difference play in wave reflection on a string?

The phase difference between the incident and reflected waves on a string is crucial in determining the intensity of the reflected wave. When the phase difference is 180 degrees, the reflected wave will be in phase with the incident wave, resulting in constructive interference and a higher intensity. A phase difference of 0 degrees will result in destructive interference and a lower intensity.

4. How does the length of a string affect wave reflection?

The length of a string affects wave reflection by altering the wavelength of the wave. A longer string will result in a longer wavelength, which in turn changes the phase difference between the incident and reflected waves. This change in phase difference affects the intensity of the reflected wave, resulting in a different pattern of constructive and destructive interference.

5. What is the relationship between wave reflection and phase difference?

The relationship between wave reflection and phase difference can be summarized as follows: a phase difference of 180 degrees results in constructive interference and a higher intensity of the reflected wave, while a phase difference of 0 degrees results in destructive interference and a lower intensity. The phase difference is influenced by factors such as the mass and length of the string, which in turn affect the speed, wavelength, and frequency of the wave.

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