# Superposition Principle and Interference

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Applets and Animations
Videos

Student Learning Objectives

• To understand and use the principle of superposition.
• To understand the difference between constructive and destructive interference.
• To understand the concept of diffraction.
• To calculate the beat frequency for two sources with nearly equal frequencies.
• To understand how standing waves are generated.
• To understand the basic properties of standing waves.
• To calculate the allowed wavelengths and frequencies of standing waves on strings.
• To calculate the allowed wavelengths and frequencies of standing sound waves in tubes and pipes.

Lessons / Lecture Notes

The Physics Classroom (conceptual)

PY105 Notes from Boston University (algebra-based):

Introductory physics notes from University of Winnipeg (algebra-based):

HyperPhysics (calculus-based)

PHY2048 notes from Florida Atlantic University (calculus-based):

General Physics I notes from ETSU (calculus-based)

Important Equations

Example Problems

Problem 1
Two loudspeakers are vibrating in phase. They are set up as in the figure below, and point C is located as shown there. The speed of sound is 343 m/s. The speakers play the same tone. What is the smallest frequency that will produce destructive interference at point C? (Solutions)

Problem 2
(a) A cello string has a fundamental frequency of 65.40 Hz. What beat frequency is heard when this cello string is bowed at the same time as a violin string with frequency of 196.0 Hz? (Hint: The beats occur between the third harmonic of the cello string and the fundamental of the violin.)

(b) A tube 1.20 m long is closed at one end. A stretched wire is placed near the open end. The wire is 0.330 m long and has a mass of 9.60 g. It is fixed at both ends and oscillates in its fundamental mode.  By resonance, it sets the air column in the tube into oscillation at the tubes fundamental frequency. Find that frequency and the tension in the wire. (Solutions)

Applets and Animations