Answer :
Final answer:
There are 24 independent standing waves with wavelengths between 9.5 and 10.5 mm and 240 with wavelengths between 99.5 and 100.5 mm.
Explanation:
To determine the number of independent standing waves with wavelengths between 9.5 and 10.5 mm that can occur in a cubical cavity 1 m on a side, we need to calculate the range of wavelengths that can fit within the given range.
The minimum wavelength within the range is 9.5 mm (0.0095 m) and the maximum wavelength is 10.5 mm (0.0105 m).
To find the number of standing waves within this range, we can calculate the number of quarter wavelengths that can fit within the length of the cavity and subtract 1. Since a cube has 6 sides, we multiply by 6 to account for all possible orientations of the standing waves.
The number of standing waves with wavelengths between 9.5 and 10.5 mm is therefore (4 * 1) * 6 = 24.
Similarly, to calculate the number of standing waves with wavelengths between 99.5 and 100.5 mm, we use the same method and find that the number is (4 * 10) * 6 = 240.
