Short on time? This page is the recap. For explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- A wave pulse is a single disturbance. A wave is a continuous, periodic disturbance with a definite wavelength and frequency.
- Both move energy from one place to another. Each part of the medium only moves around its equilibrium position.
- Mechanical waves (strings, water, sound) need a medium. Electromagnetic waves (light, radio) do not.
- Transverse: disturbance perpendicular to the direction of travel. Longitudinal: disturbance parallel to it.
- Sound is a mechanical, longitudinal wave. Compressions are high-pressure regions; rarefactions are low-pressure regions.
- Amplitude = maximum displacement from equilibrium. For sound, it can be the largest pressure change from normal pressure.
- Larger amplitude means more energy and, for sound, a louder sound.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| v = √(F_T/μ) | F_T tension in N; μ = m/ℓ in kg/m; v in m/s | find or compare pulse speeds on a string |
| μ = m/ℓ | m in kg, ℓ in m | get mass per length from a mass and a length |
| t = d/v | d in m | find a travel time |
| c = 3.00 × 10⁸ m/s | all EM waves in a vacuum | compare light and sound travel times |
| Change | Effect on speed |
|---|---|
| Tension × 4 | speed × 2 |
| Mass per length × 4 | speed × ½ |
| Amplitude × 2 | no change |
| Warmer air (sound) | faster |
Assumptions behind the numbers
- Strings are uniform (μ is the same everywhere) and the tension is constant along the string.
- The speed does not depend on the amplitude or on the shape of the pulse.
- Sound speed figures are for a stated medium and temperature.
Mistakes to avoid
- Saying the medium travels with the wave. Only energy travels.
- Forgetting the square root. Double F_T gives √2 times the speed, not twice.
- Using grams, or total mass, for μ. Use kg, and divide by length.
- Measuring amplitude crest to trough. Measure from equilibrium.
- Sending sound through a vacuum. Sound needs a medium.
- Calling a wave longitudinal because it is horizontal. Compare the disturbance with the direction of travel.
Quick self-check
- The tension in a string is made four times larger. What happens to the pulse speed? (It doubles.)
- A string has μ = 0.010 kg/m and a tension of 25 N. Find the pulse speed. (50 m/s)
- Which of these can cross empty space: sound, light, a pulse on a spring? (Only light.)
- In a sound wave, is a compression a region of high or low pressure? (High.)
Next: practice questions.