New wave after superposition (interference)

In summary, the conversation discusses standing waves formed by the superposition of two waves, and their displacement equation. It also brings up the questions of how to determine constructive or destructive interference, and whether the waves are longitudinal or transverse. The conversation suggests looking up trigonometric identities for a starting point and discusses the concept of superposition.
  • #1
Helly123
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Homework Statement


1. Homework Statement [/B]
The displacement y of standing wave that is obtained by a superposition of waves :
Y1 = 3 sin (2##\pi##(0.5t - 0 25 x))
Y2 = 3 sin (2##\pi##(0.5t + 0 25 x))

Homework Equations


Formula for standing waves
Y = 2Asinkx coswt

The Attempt at a Solution


Y1 going to right
Y2 going to left
Both have different direction.

How to decide it is constructive or destructive interference?
Are they longitudinal or transverse waves? Does it matter?

How to know in the new equation, which belong to sin x or t variable, which belong to cos?
 
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  • #4
You should be able to find these on your own. Look under Sum-to-product.
 
  • #5
kuruman said:
You should be able to find these on your own. Look under Sum-to-product.
Oh. So superposition is y1 + y2 ?
Why superposition not happen to be y1 - y2?
How to know if both waves get destructive or constructive interference?
 

Related to New wave after superposition (interference)

1. What is "New wave after superposition (interference)"?

"New wave after superposition (interference)" refers to the phenomenon in which two or more waves overlap and combine to form a new wave with a different amplitude, frequency, or direction of propagation. This interference can be either constructive, resulting in a wave with greater amplitude, or destructive, resulting in a wave with lower amplitude or cancellation of the waves.

2. What causes interference in new wave after superposition?

Interference in new wave after superposition is caused by the interaction of two or more waves with each other. When waves with the same frequency and amplitude meet, their peaks and troughs align and combine to form a new wave. This can also occur with waves of different frequencies, resulting in a complex interference pattern.

3. How is interference in new wave after superposition observed?

Interference in new wave after superposition can be observed in various ways, such as in water waves, sound waves, and light waves. In water waves, interference can be seen as the formation of larger or smaller waves due to the combination of smaller waves. In sound waves, interference can be heard as beats or changes in volume. In light waves, interference can be observed as the formation of bright and dark fringes, as seen in the double-slit experiment.

4. What is the significance of interference in new wave after superposition?

The significance of interference in new wave after superposition lies in its ability to create new waves with different properties. This allows for the manipulation and control of waves in various applications, such as in technology, communication, and medical imaging. It also provides valuable insights into the nature of waves and their behavior.

5. Are there any real-life examples of interference in new wave after superposition?

Yes, there are many real-life examples of interference in new wave after superposition. One example is the use of noise-canceling headphones, which work by creating a new wave that interferes with the incoming sound waves, effectively canceling out the noise. Another example is the colorful patterns seen in soap bubbles, which are a result of interference between light waves reflecting off the inner and outer surfaces of the bubble. Additionally, interference plays a crucial role in the functioning of electronic devices, such as antennas and radios.

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