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Reflection of String Waves

Have you ever done skipping? Have you seen how the rope moves- this movement of the rope can be used as an example to help you understand the wave movement. But what’s the reason behind such movement of the rope? It’s because of the standing wave. But what is a standing wave? Here in the section below, we’ll help you understand the concept of standing wave for you gather better clarity on the same.

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Reflection of String Waves

What happens to an object, supposedly, a ball when it is thrown against a hard wall? Yes, bounces back. This can be termed as “reflection” experienced by the object. As physics, this aspect can be measured in terms of energy and momentum conservation. In another case, if the collision involving the ball and wall is effortlessly elastic, then, in this case, the incident energy, as well as momentum, is returned. In simple terms, the object or ball will bounce back at the same speed. Furthermore, if the collision tends to be inelastic, the wall (or ball) would absorb a share of the momentum and incident energy. Therefore, the ball wouldn’t bounce back at the same speed.

It is important to note that, waves also carry energy and momentum. Hence, whenever a wave bumps into an obstacle, there is a tendency to reflect after the collision. Some of the well-known wave phenomena such as echoes are a result of reflection of waves. Furthermore, the generation of standing wave is also a result of this wave reflection. Do string waves reflect? Let us know about this.

Wave Pulse Propagation on a String

Under this situation, a wave pulse is traveling on a string. Here, the speed is denoted by ‘c’; it is the pace with which the wave pulse propagates along the string based on the elastic restoring force (tension, T) as well as inertia (mass per unit length, μ). The equation is determined as:

c = √(T/μ)

Rigid Boundary Reflection of String Wave

Here, the wave pulse over a string propagates from left to right reaching the end where it is rigidly clamped. The moment the wave pulse reaches the fixed destination, the internal restoring forces would permit the wave to broadcast an upward force on the terminal of the string. However, since the terminal is clamped, there is no chance it can move.

Hence, based on Newton’s third law, the rigid wall might be applying an equal downward force toward the string end. As a result of this new force, a wave pulse is generated that transmits from right to left. It carries amplitude and its speed is similar to the incident wave but holds opposite polarity.

Soft Boundary Reflection of String Wave

As per this condition, the string propagates from left to right directed towards the end of the string that is free to move upright or vertically. Further, the net vertical force present at the free end should be zero. Also, the slope of the string-displacement needs to be zero, specifically, at the free end for proving this boundary condition mathematically.

Hence, the reflected pulse wave propagates in the direction right to left, having the same speed & amplitude like the incident wave. The polarity, in this case, remains the same.

Resonance & Standing Wave

The concept of resonance can be linked to wave phenomena. In a wave medium, resonance (such as on a string) is standing wave. In simple words, they are equivalent to the resonant oscillation of a spring and mass. Furthermore, a stretched string can comprise of many frequencies, unlike the spring and mass that holds only a single resonant frequency. These diverse frequencies are termed as harmonic series; and are accountable for the generation of tones in a guitar, piano etc.

Whenever energy is transferred to the strings present in these instruments, they tend to oscillate at the unusual frequencies from the harmonic series. If you watch the movement of the string while vibrating at one of the specific frequencies from the harmonic series, you can analyze a standing wave pattern. This is different for every frequency mentioned under the harmonic series.

Question For You

Q. What do you understand by Standing Wave?

Ans: A standing wave is a particular type of wave that can only be formed when a wave’s motion is controlled by a fixed region. In order to understand this, let’s think about a vibrating guitar string. The motion of the guitar string is confined on both terminals of the string, where it actually associates to the guitar’s body. Hence, whenever you pluck the string, the wave reflects from each of these defined boundaries.

In a standing wave, the incident wave and reflected wave meet, where both waves hold zero amplitude. Hence, as the waves proceed to move past each other, they tend to interfere either constructively or destructively.

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