Final answer:
The mode of the standing wave is m = 1 and there will be 7 antinodes if the frequency is increased to 7f0.
Step-by-step explanation:
The mode (m-value) of a standing wave on a string is determined by the number of half-wavelengths that fit on the string. Each half-wavelength corresponds to an antinode. In the figure, the standing wave has one antinode, which means it has half of a wavelength, so the mode is m = 1.
If the frequency is increased to 7f0, the number of antinodes will also increase. The frequency of a standing wave is directly proportional to the number of antinodes it has. Since the frequency is multiplied by 7, the number of antinodes will also be multiplied by 7. Therefore, there will be 7 antinodes.