# Reflection of inverted waves to form a standing wave

• Vivek98phyboy
In summary, standing waves in a string fixed at one end can be formed by incoming and reflected waves, even if the reflected waves are 180° out of phase with the incoming wave. This is because the phase shift is different at each point due to the opposite directions of the waves, resulting in complete destructive interference at the anti-nodes of the standing wave.
Vivek98phyboy
Standing waves in a string fixed at one end is formed by incoming and reflected waves. If reflected waves are 180° out of phase with incoming wave, how could they combine to give an oscillating wave? Shouldn't it be completely destructive interference all the time across the whole length of string?

Vivek98phyboy said:
Shouldn't it be completely destructive interference all the time across the whole length of string?
Clearly not, because we get standing waves.

Have you tried writing down an expression for the sum of two waves moving in opposite directions?

Dale
Vivek98phyboy said:
If reflected waves are 180° out of phase with incoming wave, how could they combine to give an oscillating wave? Shouldn't it be completely destructive interference all the time across the whole length of string?
As @Ibix says, the best and easiest way to see this is simply to write it down. Even better if you have plotting software you can use.

Vivek98phyboy said:
Standing waves in a string fixed at one end is formed by incoming and reflected waves. If reflected waves are 180° out of phase with incoming wave, how could they combine to give an oscillating wave? Shouldn't it be completely destructive interference all the time across the whole length of string?
No, because they are traveling in opposite directions, so the phase shift is different at each point. The interference is completely destructive at the anti-nodes of the standing wave.

## 1. How do inverted waves reflect to form a standing wave?

When an inverted wave meets a normal wave, they combine and form a standing wave. The inverted wave has the same amplitude but opposite direction as the normal wave, resulting in a stationary pattern.

## 2. What causes the formation of a standing wave?

A standing wave is formed when two waves with the same frequency and amplitude travel in opposite directions and meet at a fixed point. This results in the waves interfering with each other and creating a stationary pattern.

## 3. What is the difference between a standing wave and a traveling wave?

A standing wave does not propagate or travel through space, whereas a traveling wave moves from one point to another. In a standing wave, the energy is transferred back and forth between the two waves, while in a traveling wave, the energy moves in the direction of the wave.

## 4. How does the wavelength of a standing wave compare to that of a traveling wave?

The wavelength of a standing wave is twice the distance between two consecutive nodes (points of zero amplitude). This is because the standing wave is created by the interference of two waves with the same wavelength traveling in opposite directions. In contrast, the wavelength of a traveling wave is the distance between two consecutive crests or troughs.

## 5. What are some real-life examples of standing waves?

Standing waves can be observed in musical instruments, such as a guitar string or a pipe organ, where the vibrations of the string or air column create a standing wave. They can also be seen in water bodies, such as a lake or a swimming pool, when two waves meet and create a stationary pattern. Standing waves are also used in medical imaging techniques, such as ultrasound, to create images of internal organs.

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