I REALLY JUST WANT TO UNDERSTAND THIS TYPE OF PROBLEM - ANY HELP AT ALL ON THIS WOULD BE AMAZING:

Standing waves on a string are generated by oscillations having amplitude 0.005 m, angular frequency 942 rad/s, and wave number 0.750π rad/m.
a.) What is the equation of the standing wave?
b.) At what distances from x=0 are the nodes and antinodes?
c.) What is the frequency of a point on the string at an antinode?
d.) If the string is 4m long, how many nodes are there?

Question

I REALLY JUST WANT TO UNDERSTAND THIS TYPE OF PROBLEM - ANY HELP AT ALL ON THIS WOULD BE AMAZING:

Standing waves on a string are generated by oscillations having amplitude 0.005 m, angular frequency 942 rad/s, and wave number 0.750π rad/m.  
a.) What is the equation of the standing wave?
b.) At what distances from x=0 are the nodes and antinodes?
c.) What is the frequency of a point on the string at an antinode?
d.) If the string is 4m long, how many nodes are there?

anonymous · Answer

1)$$s=2*0.005*\sin(0.75\Pi*x)\cos(942*t \pm \Pi/2)$$
2) wave length $$2*\Pi/k$$
 nodes in $$x=n*\lambda/2$$
   n is natural number
4) number of nodes 
$$4/(\lambda/2) =3$$|