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 =

Question

BlackTom AI · Accepted Answer

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 =

View Explanation

Log in for full answers

Similar Questions

A string that is fixed at both ends has a length of 2.36 m. When the string vibrates at a frequency of 77.0 Hz, a standing wave with five loops is formed. What is the wavelength of the waves that travel on the string?

The first harmonic of a closed pipe of length L is 300 Hz. To play the same note on an open pipe the length of the pipe could be

The fundamental frequency of a pipe closed at one end is f. What is the frequency of the third harmonic?

A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the wave speed?

An organ pipe is closed at one end. Several standing wave patterns are sketched in the drawing. Which one is not a possible standing wave pattern for this pipe?

A string, 6.0 meters in length, is fixed at both ends and tightened until the wave speed is 100 m/s. What is the frequency of the standing wave shown in the figure?

For a standing wave formed within an open ended air column, which of the following statements describe the condition at both ends?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler