Example 2 Two waves traveling in opposite directions produce a standing
wave. The individual wave functions are
y, = 4 sin (3x - 2t)
y2 = 4 sin (3x + 2t)
where x and y are measured in centimeters and t is in seconds.
a. Find the amplitude of the simple harmonic motion of
the element of the medium located at r= 2.3 cm.
b. Find the positions of the nodes and antinodes if one
end of the string is at x = 0.
c. What is the maximum value of the position in the
simple harmonic motion of an element located at an
antinode?​

How much work is done lifting a 9.10 kg box straight up onto a shelf that is 1.80 m high?

Gas cloud 1 is likely to form a star. gas cloud 2 is not. based on this information, match the given conditions with each cloud

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin. answer in one word. part bfind e(r), the magnitude of the electric field at distance r from the point charge q. express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q. express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r