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
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
so is the answer D correct?
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.
To determine which wavelength could not make a standing wave in a 1.0 m string with nodes at both ends, we can use the formula:
wavelength = 2 * length / n
where wavelength is the distance between two consecutive nodes, length is the length of the string, and n is the number of nodes.
In this case, since the string has nodes at both ends, n will be an odd number. We can check each wavelength option to see if it satisfies this condition.
A. wavelength = 2.0 m
Here, n = 1 since there is one node at each end. Therefore, the wavelength is 2.0 m, which can form a standing wave.
B. wavelength = 1.0 m
Again, n = 1 since there is one node at each end. The wavelength is 1.0 m, and it can form a standing wave.
C. wavelength = 0.75 m
Once more, n = 1 as there is one node at each end. The wavelength of 0.75 m can form a standing wave.
D. wavelength = 0.50 m
In this case, n = 1, and the wavelength is 0.50 m. This option satisfies the condition of having one node at each end, and it can form a standing wave.
E. wavelength = 0.25 m
Again, n = 1, and the wavelength is 0.25 m. This option also satisfies the condition, and it can form a standing wave.
Therefore, based on the analysis above, the correct answer is not D (0.50 m).