Question

Which wave of the following wavelengths could not make a standing wave in a 1.0 m string, with nodes at both ends?
A. 2.0 m
B. 1.0 m
C. 0.75 m
D. 0.50 m
E. 0.25 m

i think the answer is D

Answer 1

Try to draw a wavelength of .75 meters in your 1 meter string without a crest, not a node, at one end.

D is allowed for sure, the lowest resonance. Draw it

Answer 2

so is the answer D correct?

Answer 3

No, did you read what I wrote?
You have to have an integral number of HALF wavelengths

2 m has one antinode in the middle
1 m has 2 antinodes at .25 and .75
.666666 m has 3 antinodes at 1/4, 1/2, and 3/4 (1.5 whole waves in there)
.5 m has 2 whole waves in there, 4 antinodes
.25 has 4 whole waves, 8 antinodes

.75 is impossible to draw with a node at each end.