How Do You Solve These Wave and Phase Calculation Problems?

[Ishu]

Hi, I have two question...I spent 2 hrs on these two but couldn't fins out how to solve it...can anyone show me right way? hint?

1
A sinosodial wave of frequency 500Hz has a speed of 350 m/s
a. How far apart are two points that differ in phase by Pi/3 rad?
b. What is the phase difference between two displacments at a certain point at times 1.00ms apart?


2.
the function y(x,t)= (15.0 cm) cos ((pi)x-15(pi)t) with x in meters and t in secconds, describes a wave on a taut string. what is the trasnverse speed for a point on the string at an instant when that point has the displacement y= +12.0 cm?

 

[berkeman]

1) Use units to help you work with this. Remember that Hz = 1/seconds. So what is the wavelength in meters for a 500Hz wave traveling at 350m/s? Carry the units along in your calculation the same way as you do the numbers...units in the numerator multiply together, and units in the denominator multiply together. Like, a 10Hz wave traveling at 5m/s has a wavelength of (5m/s)/(10/s) = 0.5m. See how to do that? Once you figure out what the wavelength is for the problem, that is 2*PI of its phase...

2) Do you know what is meant by transverse speed? It is motion of the string in which dimension? And speed is just the derivative of the position with respect to time...

 

[Ishu]

Hi thanks for your reply. But none of your hints were helpful. I mean I already know these stuff...But I wanted to know what to do after that?
How to relate the given values in the problem?

 

[berkeman]

Well if you know the wavelength, and a wavelength is 2*Pi radians, then how far apart would two points Pi/3 radians be apart. Seems pretty straightforward once you have the wavelength, eh?

And if you have the wavelength and linear velocity, how much phase rolls by in 1ms?

And on 2), if you understand what transverse speed is, what partial derivative of y(x,t) do you want to use to calculate that speed?

 

[Ishu]

hmm thanks... no. 1 question is making some sense..now...haha
and thnks for making it clear

and on no. 2 I tried taking devitaive before with respect to time.
it gives

dy/dt = 15.0 cm (-sin((pi)x-15(pi)t)) * ((pi)x-15(pi)))

now where a I suppiosed to plug in that given y= +12.0 cm at?

 

[Ishu]

Anyone can give me more hint??

 

[Ishu]

No one? ?