Wave on a String
Classroom worksheet · Interactive simulation: https://lkforge.com/tools/physics/wave-on-a-string/
Name: Date:
Learning objectives
- Relate wave speed, frequency, and wavelength.
- Describe how tension and linear density affect wave speed.
- Recognize standing waves and their nodes and antinodes.
Variables to change
- Frequency
- Amplitude
- Tension
- Damping
Procedure
- Drive the string at a steady frequency and measure the wavelength.
- Double the frequency and measure the wavelength again.
- Increase the tension and observe the effect on wave speed and wavelength.
- Tune the frequency until a stable standing wave (fixed nodes) appears.
Observations
Record frequency, wavelength, and computed wave speed (v = fλ) for each trial.
Questions
- Write the relationship between wave speed, frequency, and wavelength.
- When you doubled the frequency at fixed tension, what happened to the wavelength?
- How does increasing tension change the wave speed?
- What is a node? An antinode?
- What conditions produce a standing wave on a fixed string?
Answer key (instructors)
- 1. v = f·λ.
- 2. It halved, because v stays roughly constant so λ = v/f.
- 3. Wave speed increases; v = √(T/μ), so higher tension means faster waves.
- 4. A node is a point of zero displacement; an antinode is a point of maximum displacement in a standing wave.
- 5. When the driving frequency matches a resonant frequency so reflected waves reinforce, forming a stable pattern (L = n·λ/2).
A wave transfers energy along the string at speed v = √(T/μ). Since v = fλ, raising the frequency shortens the wavelength. At resonant frequencies incident and reflected waves form standing waves with fixed nodes and antinodes.