The diagrams below show two standing wave patterns that are set up in a stretched string fixed at both ends. The frequency of pattern 1 is f1 and that of pattern 2 is f2. The ratio f1/f2 =

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The problem involves standing waves on a string fixed at both ends. For such a string, the allowable frequencies are f_n = n(v/2L), where n is the mode number (n = 1, 2, 3, ...). Thus, the frequencies are integer multiples of the fundamental frequency f_1.

Option 1: 1/3. If f1/f2 = 1/3, this means f2 = 3 f1. This is consistent with pattern 2 corresponding to a higher harmonic with three times the frequency of pattern 1, which fits the idea that the second pattern could be a mode with more nodes/antinodes than the first.

Option 2: 2/3. This would imply f2 = (3/2) f1, i.e., pattern 2 is only halfway up to the next harmonic. However, on a fixed string the ratio of successive allowed frequencies should be integers (2/1, 3/1, 4/1, ...), not 3/2 when considering the simple comparison of two distinct harmonics.

Option 3: 6. This would require f2 = 6 f1, implying a very large jump in harmonic number between the two patterns. With just two standing-wave patterns shown on a single string and labeled as two consecutive patterns, such a large ratio is not consistent with the typical n-step spacing of harmonics.

Option 4: 3. This would mean f1 = 3 f2, i.e., pattern 1 would be a higher harmonic and pattern 2 the fundamental, which contradicts the idea that pattern 1 appears to be the lower-frequency (lower-mode) pattern and pattern 2 is a higher-frequency (higher-mode) pattern.

In summary, the frequency of standing-wave patterns on a fixed string scales with the mode number n, and the observed pairing of patterns typically reflects pattern 2 having a higher n than pattern 1. The ratio equal to 1/3 is the only option consistent with f_n = n(v/2L) for two distinct harmonic patterns where the first pattern corresponds to a lower n and the second to a higher n.

SPHY001 Practice Quiz - Unit 17 | LA057

The diagrams below show two standing wave patterns that are set up in a stretched string fixed at both ends. The frequency of pattern 1 is f1 and that of pattern 2 is f2. The ratio f1/f2 =

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