what is the difference between a static sine wave,a pulsating sine wave and a travelling sine wave and what are their mathematical representations?

Question

anonymous · Answer

@ganeshie8 @mathstudent55

anonymous · Answer

@kropot72

anonymous · Answer

@UnkleRhaukus @ash2326

anonymous · Answer

please help me..if I understand this my work will be easy

unklerhaukus · Answer

A traveling wave is a function of position and time,
a standing wave is a function of position (but is constant with time).

aravindg · Answer

A static sine wave is the usual sine wave we come across in problem. A pulsating one has its amplitude varying with time.

anonymous · Answer

so in a travelling wave each point experiences every amplitude from the positive maximum to negative maximum?

unklerhaukus · Answer

yeah for a travelling wave over one cycle, every point experiences the max and min

ganeshie8 · Answer

static sine wave : $$\large   y = A \sin (kx)$$

ganeshie8 · Answer

travelling sine wave with velocity $v  $, $\implies  \text{displacement  = vt}$  :
$$\large  y = A\sin(k(x-vt))$$

ganeshie8 · Answer

Clearly the wave is moving right as the transformation is shift right ^^

anonymous · Answer

@ganeshie8 y=Asin(wt) is this for pulsating sine wave?

anteater · Answer

So then for a pulsating sine wave A would just be some function that varies with t?

aravindg · Answer

Indeed!

anteater · Answer

This will probably confuse things, and I apologize, but I am curious! Would a pulsating wave necessarily be a traveling wave?

unklerhaukus · Answer

I can imaging a standing wave that is pulsating

anteater · Answer

Ok, thanks! I was thinking that A could be a constant, or a function of t. Could A also be a function of x and t? I mean if you have a sine function that is a function of two variables, couldn't the Amplitude function also be a function of both variables?

unklerhaukus · Answer

i guess so