🔖 Topics

  • Waves on a String
  • Waves in a Pipe

🎯 Objectives

  • Calculate the properties of waves on a string fixed at both ends
  • Calculate the properties of waves in a half-open pipe
  • Calculate the properties of waves in a fully open pipe

📋 Sequence

  • Review of resonance
  • Properties of waves on a string fixed at both ends
  • Properties of waves in a half-open pipe
  • Properties of waves in a fully open pipe

🖥️ Animations, Simulations, Activities

N/A

📝 Practice Problems

Resonant Frequencies: The three lowest resonant frequencies of a system are 50 Hz, 150 Hz, and 250 Hz. Which of the following setups could have these frequencies?

  1. A tube of air closed at both ends
  2. A tube of air open at one end
  3. A tube of air open at both ends
  4. A vibrating string with fixed ends

Distance Between Nodes: A pipe, closed at one end and open at the other, is one meter long. In the standing wave whose frequency is seven times the fundamental frequency, what is the distance between adjacent nodes?

Organ Pipe Beat Frequency: An auditorium has organ pipes at the front and at the rear of the hall. Two identical organ pipes, one at the front and the other at the back have fundamental frequencies of 264 Hz at 20\(^\circ\) C. During a performance, the organ pipes at the back of the hall are at 25\(^\circ\) C while those at the front are still at 20\(^\circ\) C. What is the beat frequency when the two pipes sound simultaneously?

✅ Partial Solutions

N/A

📘 Connected Resources

  • Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.