# What is the Maximum Transverse Speed and Displacement in a String Wave Equation?

• ee1215
In summary: For example, the first equation is surrounded by a single tex tag on a line by itself. The second equation is surrounded by a tex tag on a line by itself, followed by a line of source, followed by a tex tag on a line by itself.There is another way to see the source if you have a recent version of IE. However, I am not sure if it is the same for IE7 as for IE8. With IE8, just hover your mouse over the equation and you should see a "Click to activate" button appear. Click there and you should see the equation source. I think it is a bit different for IE7.About IE7 -- I think clicking on the equation
ee1215

## Homework Statement

Equation of transverse wave traveling along a string is:
y=6cm sin(0.02$$\pi$$x-4$$\pi$$t)
where x and y are in cm and t is in seconds

A)find max transverse speed of a particle in the string
B)Find transverse displacement of a particle in the string at x=3.5cm and t=0.2s

## Homework Equations

$$\mu$$max=$$\omega$$ym

y(x,t)=ym*sin(kx-$$\omega$$t)

## The Attempt at a Solution

A) I got $$\mu$$max = 4$$\pi$$*(.06m) = 0.75m/s
B) y(x,t)=0.06m*sin(.02$$\pi$$(.035m)-4$$\pi$$(0.2)) = -0.035m

Are these correct?

Copy and paste these greek letters and write an equation in one line.

ehild

I'll try fixing up the LaTeX for you:

## Homework Statement

Equation of transverse wave traveling along a string is:
$$y=6 sin(0.02{\pi}x-4{\pi} t)$$
where x and y are in cm and t is in seconds

A)find max transverse speed of a particle in the string
B)Find transverse displacement of a particle in the string at x=3.5cm and t=0.2s

## Homework Equations

$${{\mu}_max}={{\omega}_y} m$$

$$y(x,t)=y_m*sin(kx-{\omega} t)$$

## The Attempt at a Solution

A) I got $${{\mu}_max} = 4 {\pi}*(.06m) = 0.75m/s$$
B) $$y(x,t)=0.06m*sin(.02{\pi}(.035m)-4{\pi}(0.2)) = -0.035m$$

Are these correct?

EDIT -- Did I get it rendered right? [STRIKE]You can use the "Quote" button to see how I changed your LaTeX.[/STRIKE] Not sure I got your intended groupings right though. Also, aren't you supposed to get answers in cm?

EDIT2 -- See my later post for how to see the LaTeX equations in my post.

Last edited:
Yes, that is correct. Should be u max instead of the subscript of just m. But I was just wanting someone to check my answers for me. I would just convert them to cm then.

The constants in your given equation $y=6 sin(0.02{\pi}x-4{\pi} t)$ don't have units attached, but given that the problem statement specifies cm and seconds for x and t, it is (hopefully) reasonable to assume that you should have to use values specified in these implied units in the formula. That is, when you plug in 3.5 cm for x, better make it "3.5" rather than "0.035" .

If the formula had included these implied units it might look something like:
$$y(x,t) = 6cm \; sin \left( \frac{0.02 \pi}{cm}x + \frac{4 \pi}{sec}t \right)$$

berkeman said:
EDIT -- Did I get it rendered right? [STRIKE]You can use the "Quote" button to see how I changed your LaTeX.[/STRIKE] Not sure I got your intended groupings right though. Also, aren't you supposed to get answers in cm?

EDIT2 -- See my later post for how to see the LaTeX equations in my post.

Sorry, since I have your fixed-up equations in a Quote Box, you cannot click on Quote to see the source for the equations.

Instead, highlight the equation you want to see (using click-drag with your mouse), then right-click the equation and select Show Source. Expand the box to see what the equation source is -- there is a single set of tex tags around each line of source.

## 1. What is a transverse wave along a string?

A transverse wave along a string is a type of mechanical wave that travels along a string or rope by vibrating perpendicular to the direction of the wave's motion. This means that the particles of the string move up and down while the wave moves horizontally.

## 2. How is a transverse wave along a string different from a longitudinal wave?

A transverse wave moves perpendicular to the direction of the wave's motion, while a longitudinal wave moves parallel to the direction of the wave's motion. In a longitudinal wave, the particles of the medium move back and forth in the same direction as the wave.

## 3. What factors affect the speed of a transverse wave along a string?

The speed of a transverse wave along a string is affected by the tension, mass, and length of the string. The greater the tension and the lighter the mass of the string, the faster the wave will travel. However, the longer the string, the slower the wave will travel.

## 4. How is the amplitude of a transverse wave along a string related to its energy?

The amplitude of a transverse wave along a string is directly proportional to its energy. This means that the greater the amplitude, the more energy the wave carries. This can be seen in real-life scenarios, such as a guitar string producing a louder sound when strummed with greater force.

## 5. Can a transverse wave along a string be reflected and refracted?

Yes, a transverse wave along a string can be reflected and refracted. When a wave reaches the end of a string, it can bounce back and be reflected. Refraction can also occur when a wave passes from one medium to another, causing it to change direction and speed. This can be seen when a guitar string is plucked and the wave travels from the string to the air, causing a sound to be produced.

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