# Clarification for a standing wave on a string equation

• I
• rudy
In summary, the two expressions describe two different types of waves. Choice 1. describes a wave with a range of frequencies, while choice 2. describes a wave with a single frequency.
rudy
Hello,

For the 2 parts of the equation with sin, is it:
1. [...sin(kx)]sin(wt)

or is it:
2. [...sin(k)*x]sin(w)*t

Thank you

-DR

First, a friendly tip about images: use the UPLOAD button at the bottom of the posting box, then use the option to display as a full image instead of a thumbnail. Then people can see the image directly and don't have to click the link to access your Google Drive.

rudy said:
Hello,

For the 2 parts of the equation with sin, is it:
1. [...sin(kx)]sin(wt)

or is it:
2. [...sin(k)*x]sin(w)*t

Thank you

-DR
I am unable to understand what actually is you doubt regarding the standing waves, please make it clear in the post.

Sorry about that... I did try to upload but when I previewed my post I kept getting a "broken image link" symbol (does the image only appear once the post is published?)

And to clarify my question, I was wondering if the variables (x and t) are included inside the sine function parenthesis or if it is multiplied separately.

I'll rewrite 2. as:
[...x*sin(k)]t*sin(w)

and 1. was:
[...sin(kx)]sin(wt)

thanks jt

rudy said:
Sorry about that... I did try to upload but when I previewed my post I kept getting a "broken image link" symbol (does the image only appear once the post is published?)

And to clarify my question, I was wondering if the variables (x and t) are included inside the sine function parenthesis or if it is multiplied separately.

I'll rewrite 2. as:
[...x*sin(k)]t*sin(w)

and 1. was:
[...sin(kx)]sin(wt)

thanks jt
1 is right, the variables x and t should be within the sine function parenthesis.

If you look at 1., it describes a function that has k cycles per metre and a time variation that's proportional to ω. This describes a function with a range of frequencies and nodes.; it looks like a wave of some sort. The other expression (2.) has the k and ω inside the sin functions. These are both constants and so are sin(k) and sin(ω) so it doesn't describe a function that varies at all! It can't be a wave.
It's important to try to interpret what a formula actually does when you can. It gives a good insight into the relationship between the Maths and the Physics of a situation. It can be worth while even when some of the functions are not familiar.

## 1. What is a standing wave on a string equation?

A standing wave on a string equation is a mathematical representation of a wave pattern that remains stationary in space and does not travel through a medium. It is formed when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other.

## 2. What are the variables in a standing wave on a string equation?

The variables in a standing wave on a string equation include the wavelength (λ), frequency (f), amplitude (A), and speed of the wave (v). These variables are related by the equation v = fλ, where v is the speed of the wave.

## 3. How is a standing wave on a string equation derived?

A standing wave on a string equation can be derived using the principles of wave interference and superposition. By considering the wave equation, which describes the relationship between the wave speed, frequency, and wavelength, and applying the concept of standing waves, the equation can be derived.

## 4. What is the significance of a standing wave on a string equation?

A standing wave on a string equation is significant because it helps us understand the behavior of waves and the properties of a medium. It also has practical applications in fields such as acoustics, music, and telecommunications.

## 5. How is a standing wave on a string equation used in real-world situations?

A standing wave on a string equation is used in various real-world situations, such as in musical instruments like guitars and violins, where the strings vibrate at specific frequencies to produce different notes. It is also used in telecommunications to transmit information through cables and in medical imaging techniques like ultrasound.

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