Education

# Can I Start Class 11 Physics with Oscillations and Waves?

Theory

An oscillation is merely a motion that repeats itself (imagine a swinging pendulum); a wave is simply an oscillation that moves (imagine a pendulum that always pays attention in class, asks meaningful questions, and receives straight A’s). We’ll talk about oscillations and waves in which the oscillating object’s position graph is a sine or cosine wave; this is simple harmonic motion (SHM). SHM is further distinguished by the recurrent conversion of potential energy to kinetic and then back to potential. Returning to our pendulum, the gravitational potential energy of the pendulum grows as you draw it back. The gravitational potential energy is converted to kinetic energy once you release go. At the bottom of the pendulum’s oscillation, the kinetic energy is at its highest; as the pendulum moves upward, the kinetic energy is converted back to gravitational potential energy.

As we turn our attention to waves, let’s keep thinking about energy. Let’s imagine you throw a stone into a pond to provide energy. The stone will upset the pond’s surface, and waves in the water will carry energy away from the pebble, which is the cause of the disturbance. Consider a single water molecule that fell a little distance away from the stone. As the wave passes by this water molecule, it will be pushed higher (gaining potential energy), then downward; it will pass a point of maximal kinetic energy, then gain potential energy as it is pushed below the level of the resting surface. As the wave passes, perhaps it becomes evident that this molecule is undergoing SHM! However, unlike the wave, the water does not move away from the spot where the pebble impacted; rather, the medium oscillates in situ as the wave passes through.

Traveling waves have two main characteristics: they convey energy and, when they move through a medium, they induce SHM at every point in it. (Electromagnetic waves are energy-carrying travelling waves which do not required a medium to travel.) Whatever You Need to Know About Electromagnetic Waves has a lot more information on these topics!) Another key feature of moving waves is that they may interact with one another. Let’s go back to the pond’s pebble. Your companion now tosses another pebble into the mix, a little distance from yours. The waves will ultimately converge in the same area at the same time as they spread out from the points where each pebble landed. The trough will be lower if both waves drive the water down at this location than if just one wave passes (the same principle applies if both waves push the water up). This is referred to as constructive interference. If one wave is pushing the water up and the other is pushing the water down at the point where the waves meet, the water’s surface will stay in its regular position. This is what is known as disruptive interference.

Waves in motion can also interact with one another. You send a wave down a guitar string when you pluck it. Because the front border of the waveform approaches the tuner, in which the string is secured to the guitar’s neck and therefore unable to vibrate, the wave bounces off this fixed point and returns to your fingers. Nonetheless, it runs into a section of the wave that is still making its way up the instrument’s neck. This wave and its reflection will interfere constructively in some locations and destructively in others, resulting in what is known as a standing wave. Waves will begin to reflect off boundaries at either end of the wire and collide until all of the initial energy input has been dissipated as thermal or other types of energy. (It’s worth noting that standing waves do not even have to be on a string; for example, a standing sound wave in the air between two boundaries.) We call nodes and antinodes points of complete destructive interference (where the string doesn’t move at all) and maximum constructive interference (where the string is maximally displaced from equilibrium during each cycle). Only specific standing wave sizes (technically, wavelengths — we’ll talk about this more later) are allowed for a particular wave speed and border separation distance. These permissible states are referred to as modes. The number of antinodes in a standing wave is the same as its mode number m.