One equation for every travelling wave

Science · Waves, Light & Sound · ages 18-19

Name ______________________ Date ____________

For y equals A sin of kx minus omega t, what is the speed?
- k over omega
- A times omega
- omega over k
Which form travels undistorted at speed v?
- f of x minus vt
- f of x times vt
- f of x plus v plus t
Only sine shapes can travel without distortion.
Circle one: True False
Sound in air is which kind of wave?
- Transverse, shaking across travel
- Longitudinal, shaking along travel
- Still, with no shaking at all
Sound moves at 340 metres per second from a 170 hertz source. What is the wavelength in metres?
Answer: ______________
How do you check a candidate function against the wave equation?
- Differentiate twice each way and compare
- Measure its amplitude once
- Count its peaks by eye
For y equals 3 sin of 2x minus 6t, what is the speed?
- 4
- 3
- 12
A student reads the speed as k over omega. What is the error?
- Speed equals the amplitude A
- Speed needs a square root
- Speed is omega over k, the ratio is flipped

Answer key

For grown-ups. Fold this page away before handing over the rest.

omega over k · Speed is the time rate over the space rate.
f of x minus vt · Only the pair x minus vt glides rigidly forward.
False · Any twice bendable shape in x minus vt passes the test.
Longitudinal, shaking along travel · Air compresses along the travel direction.
2 · Lambda equals v over f, so 340 over 170 is 2.
Differentiate twice each way and compare · The test compares second derivatives in time and space.
3 · Omega is 6 and k is 2, so 6 over 2 is 3.
Speed is omega over k, the ratio is flipped · The time rate sits on top, so flipping gives one over v.