Waves
Introduced| English | Meaning |
|---|---|
| wave/weɪv/ | A disturbance or oscillation that transfers energy without a net transfer of matter over the full cycle. |
| wavelength/ˈweɪvleŋθ/ | The distance between corresponding points on successive waves. |
| frequency/ˈfriːkwənsi/ | The number of complete cycles per unit time. |
| speed/spiːd/ | The rate at which a wave disturbance or a point of constant phase travels. |
| transverse waves/trænsˈvɜːs weɪvz/ | A wave whose oscillations are perpendicular to its direction of energy transfer. |
| longitudinal waves/ˌlɒŋɡɪˈtjuːdɪnl weɪvz/ | A wave whose oscillations are parallel to its direction of energy transfer. |
| electromagnetic spectrum/ɪˌlektrəʊməɡˈnetɪk ˈspektrəm/ | The complete range of electromagnetic radiation, ordered by frequency or wavelength. |
One string point moves while the pattern travels
- In a supplied string-wave model, a marked point oscillates up and down while the disturbance travels horizontally. A wave 波 transfers energy; the marked point does not travel permanently with each crest.
- The oscillation and propagation directions are different information. Their perpendicular relation makes this a transverse case; a page arrow alone would not establish wave type.
In the supplied string-wave model, what travels along the string while a marked point oscillates?
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Distinguish medium-point motion from disturbance propagation in the stated model. Do not turn this into a claim that real water surfaces can never also have currents or drift.
Define wavelength, frequency and amplitude
- Wavelength 波长 is the spacing between successive same-phase points, such as neighbouring crests. Frequency 频率 counts complete oscillations per second.
- Amplitude is maximum displacement from equilibrium. Crest-to-trough height is twice amplitude; neither measurement is the spacing between crests.
Crest-to-trough height is the same defined quantity as the spacing between successive crests.
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False: the first is twice amplitude; crest spacing is wavelength.
Calculate speed from compatible quantities
- Wave speed 波速 follows $v=f\lambda$. Supplied $f=5.0\ \text{Hz}$ and $\lambda=0.40\ \text{m}$ give $v=5.0\times0.40=2.0\ \dfrac{\text{m}}{\text{s}}$.
- Hertz means complete oscillations per second. Use wavelength in metres for this speed unit; converting 40 cm to 0.40 m before multiplying avoids a factor-of-100 error.
A wave has frequency 250 Hz and wavelength 1.4 m. What is its speed in m/s?
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Use v = fλ. The supplied values give v = 250 × 1.4 = 350 m/s. That alone does not identify the wave as sound or its medium.
Calculate period and interpret the result
- Period is time for one complete oscillation: $T=1/f=1/5.0=0.20\ \text{s}$. This is not time for a marked point to travel one wavelength along the string.
- With amplitude 0.030 m, crest-to-trough height is $H=2A=2\times0.030=0.060\ \text{m}$. This is distinct from wavelength 0.40 m; changing amplitude alone does not specify a new frequency.
A separate question supplies 250 Hz and 1.4 m. Its calculation is $v=f\lambda=250\times1.4=350\ \dfrac{\text{m}}{\text{s}}$. These two quantities do not identify the wave as sound or specify its medium.
The supplied string wave has frequency 5.0 Hz. What is its period in seconds?
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T = 1/f = 1/5.0 = 0.20 s.
Amplitude is 0.030 m. What crest-to-trough height is predicted in metres?
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H = 2A = 2 × 0.030 = 0.060 m.
Compare types using both directions
- Transverse waves 横波 oscillate perpendicular to propagation; longitudinal waves 纵波 oscillate parallel, as in a compression wave along a spring or sound in air.
- The electromagnetic spectrum 电磁波谱 extends from radio to gamma rays. Electromagnetic waves need no material medium and share a vacuum speed; this does not give mechanical waves that same speed.
Match each wave type to an example.
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Transverse oscillates across the direction of travel; longitudinal oscillates along it.
Radio waves and X-rays travel at the same speed in a vacuum.
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Electromagnetic waves share the vacuum speed while having different frequencies and wavelengths. The statement is about vacuum, not every material medium or mechanical wave.
Check the equation and the stated conditions
- Write the required equation in symbols, convert units, calculate, then state what the result measures. A value 350000 instead of 350 for the separate question signals a calculation or conversion issue to investigate.
- Keep oscillation direction, propagation, amplitude, wavelength, period and speed distinct. State the medium and conditions before comparing speeds; real water may also have currents or drift beyond an ideal wave model.
Use $v=f\lambda$, $T=1/f$ and $H=2A$ for different questions. Do not replace a mechanical-wave result with electromagnetic vacuum speed.
You calculate the supplied 250 Hz, 1.4 m wave as 350000 m/s. What calculation or units would you check?
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Example: “I would check the wavelength conversion and multiplication, because 250 Hz times 1.4 m gives 350 m/s.”