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3. A string is clamped at both ends and plucked so it vibrates in a standing mode between two extreme
positions a and b. Let upward motion correspond to positive velocities. When the string is in position c,
the instantaneous velocity of points along the string
a. is positive everywhere
b. is zero everywhere
c. is negative everywhere
d. depends on the location along the string.

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Step 1

At position c, the string is flat. So here some of the points will move up and some other point moves down. We know that the velocity of any particular point depends on where it is located. Thus the instantaneous velocity of points along the string depends on the location of the points.

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