A string has a length of 84 cm. The string is stretched taut, and both ends are restricted to be nonmoving. Touching the string at which of the following points will not produce a standing wave when the string is plucked?

No choices.

Perhaps this is more physics.

36

To determine the points at which a standing wave will not be produced when plucking a string, we need to consider the nodes and antinodes of the standing wave pattern.

In a standing wave pattern on a string, the nodes are the points where the string does not move, while the antinodes are the points of maximum displacement. For a string of length L, the standing wave pattern will have nodes at both ends (0 and L) and antinodes at the midpoint (L/2) and other harmonically related fractions of the string length.

To find which points will not produce a standing wave, we first need to determine the possible fractions of the string length. Since the string has a length of 84 cm, the possible fractions can be found by dividing the length by integers greater than 1.

By dividing the string length (84 cm) by integers greater than 1, we get the following fractions:

84/2 = 42 cm (L/2)
84/3 = 28 cm
84/4 = 21 cm
84/5 = 16.8 cm
84/6 = 14 cm
84/7 = 12 cm
84/8 = 10.5 cm
...

Now we can compare these fractions to the possible points where the string can be touched. If any of the points coincide with the calculated fractions, they will be nodes, and plucking the string at those points will not produce a standing wave.

For example, if we consider touching the string at the 28 cm point, which corresponds to the fraction 84/3, it will be a node, and therefore, no standing wave will be produced if the string is plucked at that point.

Similarly, if we find any other point that coincides with the calculated fractions, it will also be a node, and plucking the string at that point will not produce a standing wave.

Therefore, we need to compare the given points (not mentioned in the question) with the calculated fractions to determine which one will not produce a standing wave.