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Physics · 07 / 12

Waves: propagate a disturbance

High school · intermediate · Worked example and 4 exercises with solutions, at your pace.

Need a foundation?Units: numbers have dimensionsEquations: keep the balance level
UnderstandSee an exampleGuided exercise3 progressive challenges

The principle, simply

A wave carries a disturbance, without bulk transport of matter in the usual mechanical-wave model. Period is time per cycle; frequency is cycles per second. Wavelength is spatial separation. At speed v, λ = v/f and T = 1/f. Amplitude is a separate quantity.

lambda=v/f
THE PICTURE TO REMEMBERWaves: propagate a disturbance
A spatial profile gives wavelength λ between successive identical phases. A time trace at one point gives period T. Wave speed is v = λ/T.λProfile at one moment

A spatial profile gives wavelength λ between successive identical phases. A time trace at one point gives period T. Wave speed is v = λ/T.

  1. 01Disturbance
  2. 02Propagation
  3. 03Period and frequency
  4. 04Wavelength

WORKED EXAMPLE

From principle to reasoning

v = 340 m/s and f = 170 Hz give λ = 2 m and T ≈ 0.00588 s. Adjacent crests at one instant are 2 m apart.

Solve a problem in this subject

  1. Draw the system

    Define the studied object, reference frame and positive axis. A force diagram shows external interactions acting on the system.

  2. Sort quantities

    Separate data and unknowns; convert units before substitution. 36 km/h = 10 m/s, so never insert 36 into a formula expecting SI speed.

  3. Write the model

    Choose a law matching assumptions: constant acceleration, thin lens, ohmic resistor. Isolate the unknown symbolically before rounding.

  4. Interpret

    Check dimensions and signs. Negative velocity gives direction on the chosen axis. Discuss scale and model limitations.

YOUR TURN

01 · Try before checking

At fixed speed, what happens to λ if frequency doubles?

One hint

Inspect the denominator in v/f.

Reveal and understand the solution

Wavelength and period halve; amplitude is not determined by this change.

Compare method, conditions and answer; identify the exact part to revisit.

IMPROVE THROUGH PRACTICE

Three additional challenges with solutions

Start with the first challenge. Write your method before opening a hint; use the solution to find the first step that needs work.

Reflect after practising
02 · Recognise and understandLink to this exercise

A wave has period 0.02 s. Find its frequency.

A hint to get started

Frequency is the reciprocal of period.

Step-by-step solution
  1. f = 1/T.
  2. f = 1/0.02 = 50.
  3. The frequency is 50 Hz.

Which step did you miss? Retry without help, then explain why the method works.

03 · Apply the methodLink to this exercise

A wave travels at 340 m/s with f = 170 Hz. Find its wavelength.

A hint to get started

Use v = λf.

Step-by-step solution
  1. λ = v/f = 340/170.
  2. λ = 2 m.
  3. Wavelength is a spatial distance, not a duration.

Which step did you miss? Retry without help, then explain why the method works.

04 · Go furtherLink to this exercise

A wave keeps frequency 100 Hz while speed changes from 200 to 300 m/s in another medium. What happens to λ?

A hint to get started

The source fixes frequency; wavelength follows speed.

Step-by-step solution
  1. Before: λ = 200/100 = 2 m.
  2. After: λ = 300/100 = 3 m.
  3. Wavelength increases without a frequency change in this model.

Which step did you miss? Retry without help, then explain why the method works.

The trap to avoid

Distinguish a time graph from a position graph.

Without notes, can you…

  • Explain the principle in your own words?
  • Rebuild the diagram and its connections?
  • Solve the exercise and justify the method?

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