Unit 16: Waves
Transverse and longitudinal waves, interference, and the standing waves that form when two traveling waves meet head-on.
6 topics · 20 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Transverse and Longitudinal Waves
- How it worksHow do transverse and longitudinal waves differ in which way their particles move relative to the wave's direction?
- Common mistakeWhy doesn't a wave traveling across water actually carry the water itself along with it?
- Going furtherWhat happens to a slinky's coils as a longitudinal wave compresses and stretches its way down its length?
Your turn1 of 2
A cork floats on a pond as a wave passes beneath it. What does the cork actually do as the wave goes by?Wave Speed on a String
- How it worksHow do tension and mass per unit length combine to set the speed of a wave traveling along a string?
- Worked exampleFind the speed of a wave on a string with tension 40 N and linear mass density 0.005 kg/m.
- Common mistakeWhy doesn't a wave's speed on a string depend on how big an amplitude you shake it with?
Your turn1 of 2
A string has tension T and linear mass density mu. Write an expression, in terms of T and mu, for the speed of a wave on it.Mathematical Description of a Wave
- How it worksHow do wavelength, frequency, and wave speed combine into y(x,t) = A sin(kx - omega t)?
- Worked exampleFind the wavelength of a wave with frequency 50 Hz traveling at 20 m/s.
- Common mistakeWhy doesn't a wave's frequency change at all when the wave passes from one medium into another?
- Going furtherWhat happens to a wave's wavelength, but not its frequency, once it enters a medium where it travels more slowly?
Your turn1 of 2
A wave has frequency 142 Hz and travels at 34 m/s. What is its wavelength, in meters?Superposition and Interference
- How it worksHow does the principle of superposition let you just add two overlapping waves point by point?
- Common mistakeWhy doesn't destructive interference destroy any energy, even though a wave momentarily vanishes at some points?
- Going furtherWhat happens to an interference pattern from two sources as you move from a constructive point toward a destructive one?
Your turn1 of 2
Two waves interfere destructively at a certain point in space, so the disturbance there is essentially zero. What has happened to the energy that was in those two waves?Standing Waves on a String
- How it worksHow do two waves traveling in opposite directions add up to create a standing wave with fixed nodes and antinodes?
- Worked exampleFind the fundamental frequency of a 0.6 m string fixed at both ends with a wave speed of 200 m/s.
- Common mistakeWhy doesn't a standing wave actually travel anywhere, even though it's built from two traveling waves that do?
- Going furtherWhat happens to a string's allowed standing-wave frequencies if you double the string's length?
Your turn1 of 2
A string of length 1.48 m, fixed at both ends, carries waves at a speed of 212 m/s. What is its fundamental frequency, in hertz?Wave Energy and Power
- How it worksHow does the energy carried by a wave depend on the square of its amplitude?
- Worked exampleFind how the power carried by a wave changes if its amplitude is tripled, given power scales with amplitude squared.
- Ties togetherHow does a wave's energy scaling with amplitude squared connect to the same square-law you'll meet in sound intensity?
Your turn1 of 2
The power carried by a wave scales with the square of its amplitude. If the amplitude is multiplied by a factor of 3.94, by what factor does the power change?