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

 

[ehild]

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

ehild

 

[berkeman]

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.

 

[ee1215]

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.

 

[gneill]

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]

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.