Which frequency corresponds to the standing wave with the greatest number of nodes?270 Hz180 Hz 90 Hz540 Hz

1. Break Down the Problem

To determine the frequency that corresponds to the standing wave with the greatest number of nodes, we need to understand the relationship between frequency, wavelength, and the number of nodes in a standing wave. The number of nodes increases with frequency.

2. Relevant Concepts

• Standing Waves and Nodes: The number of nodes in a standing wave pattern is related to the frequency of the wave and the medium in which it travels.
• Fundamental Frequency: The fundamental frequency has the least number of nodes (2 nodes for a string fixed at both ends) and higher harmonics have more nodes.

3. Analysis and Detail

1. Nodes increase with harmonic frequency; thus, the greater the frequency, the more the nodes in the wave.
2. We have four frequencies to evaluate: 270 Hz, 180 Hz, 90 Hz, and 540 Hz.
3. The frequency directly affects how many wavelengths fit within a given length. Higher frequencies allow more wavelengths and hence more nodes.

4. Verify and Summarize

The frequency that will correspond to the highest number of nodes is the highest frequency value from our list.

Final Answer

The frequency corresponding to the standing wave with the greatest number of nodes is 540 Hz.