Self-Teaching SHM: Transverse Waves & Variables

In summary, the conversation discusses the concept of displacement and its relationship to variables x and t in a transverse motion. It is explained that y represents displacement, x specifies a point along the x-axis, and t represents time. The formula for a wave, y=Asin(kx +/- wt), is used as an example to understand the concept. It is clarified that x represents the position of a particular element of the string, while y changes periodically with time.
  • #1
MarcL
170
2
So, I have to self-teach myself part of my class. However, there's one part of my book I can't understad at all.

First, I would like to understand, why does a transverse motion has 3 variable, y,x, and t . In my book they give the explanation y=h(x,t) and when we find the formula of the wave we get y=Asin(kx +/- wt).

I'm wondering, if y is the displacement of one element of a string, then what does x represent? I'm all confused :/
 
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  • #2
Yes, y represents displacement, x specifies at what point along the x-axis. Just think about a picture of the wave... obviously displacement is not the same at every x position, and even if you stay at one x position, the displacement varies in time, hence the need for both variables.
 
  • #3
so x represent the displacement of the wave itself?
 
  • #4
No, it specifies the position in the direction that the wave is traveling. If you just have a function y(x), what does x represent? What does y represent? Nothing changes for y(x,t) except that y now changes as time passes, meaning if you say at the same x position, the displacement (y) changes (periodically, in this case). In the terms you put it, x is the position of a particular "element" of the string.
 
  • #5


I understand the frustration of trying to self-teach a complex topic. The concept of transverse motion and its variables can be difficult to grasp, but I will do my best to explain it.

First, let's define what transverse motion is. Transverse motion refers to the movement of a wave or object in a direction perpendicular to the direction of the wave or object's propagation. In the case of a transverse wave, the particles of the medium (such as a string) move up and down while the wave itself moves horizontally.

Now, let's look at the variables involved in this type of motion. The variable y represents the displacement or position of a particle on the string at a specific time t. This means that as the wave travels through the string, each particle will have a different displacement or position at any given time.

The variable x represents the position of the particle along the string. This means that each particle will have a different x-coordinate along the string.

Finally, t represents time. As the wave travels through the string, the position of each particle will change over time.

To better understand this, let's look at the formula y=Asin(kx +/- wt). The variable A represents the amplitude, which is the maximum displacement of a particle from its equilibrium position. The variable k represents the wave number, which is related to the wavelength of the wave. The variable w represents the angular frequency, which is related to the period of the wave.

So, to summarize, the variables y and t represent the displacement and time of a particle, while x represents the position of the particle along the string. Together, these variables help us understand the transverse motion of a wave on a string. I hope this explanation helps you better understand this concept. If you have any further questions, I would be happy to assist you. Keep up the hard work in your self-teaching journey!
 

1. What is SHM (Simple Harmonic Motion)?

Simple Harmonic Motion (SHM) is a type of periodic motion in which an object oscillates back and forth around an equilibrium point, following a specific pattern. This motion is characterized by a restoring force that is directly proportional to the displacement of the object from its equilibrium position, and the motion is described by a sinusoidal function.

2. What are transverse waves?

Transverse waves are waves in which the particles of the medium vibrate perpendicular to the direction of the wave propagation. This means that the disturbance is perpendicular to the direction in which the wave travels. Examples of transverse waves include electromagnetic waves and waves on a string.

3. What are the variables involved in SHM and transverse waves?

The variables involved in SHM and transverse waves include amplitude, frequency, period, wavelength, and velocity. Amplitude is the maximum displacement of the wave from its equilibrium position. Frequency is the number of complete oscillations per unit time. Period is the time it takes for one complete oscillation. Wavelength is the distance between two consecutive points on the wave that are in phase. Velocity is the speed at which the wave travels.

4. How can I teach myself SHM and transverse waves?

You can teach yourself SHM and transverse waves by first understanding the basic concepts and equations involved. Then, you can practice solving problems and performing experiments to gain a deeper understanding. There are also many online resources, such as videos and interactive simulations, that can help you learn and visualize these concepts.

5. What are some real-life applications of SHM and transverse waves?

SHM and transverse waves have many real-life applications in various fields such as engineering, physics, and biology. Some examples include the motion of a pendulum, the vibrations of a guitar string, and the movement of sound waves in air. These concepts are also used in medical imaging techniques, such as ultrasound, and in the design of earthquake-resistant structures.

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