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Wave Speed Relation v = fλ

The wave speed relation states that speed of a wave equals frequency multiplied by wavelength, written as v = fλ.

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Student-friendly explanation

In the formula v = fλ, v is wave speed in metre per second, f is frequency in hertz, and λ is wavelength in metre. It is used when any two of speed, frequency, and wavelength are given. Correct unit conversion is important, especially when wavelength is given in centimetres.

How to write this in exams

  1. 1

    Start with the exact idea

    The wave speed relation states that speed of a wave equals frequency multiplied by wavelength, written as v = fλ.

  2. 2

    Then show how to use it

    Write v = fλ. Identify given values. Convert wavelength to metre if needed. Rearrange the formula. Substitute values and write the unit.

  3. 3

    Add one concrete example

    If sound has frequency 170 Hz and wavelength 2 m, its speed is v = 170 × 2 = 340 m/s.

  4. 4

    Avoid this incomplete answer

    Wrong answer: λ = vf. This is wrong because from v = fλ, wavelength is speed divided by frequency.

Definition

The wave speed relation states that speed of a wave equals frequency multiplied by wavelength, written as v = fλ.

Example

If sound has frequency 170 Hz and wavelength 2 m, its speed is v = 170 × 2 = 340 m/s.

Rule to remember

v = fλ, where v is speed in m/s, f is frequency in Hz, and λ is wavelength in m.

Memory hook

Speed equals how often times how long each wave is.

Examples and method

Worked example

A wave has speed 330 m/s and frequency 110 Hz. Using v = fλ, λ = v/f = 330/110 = 3 m.

Method to apply

Write v = fλ. Identify given values. Convert wavelength to metre if needed. Rearrange the formula. Substitute values and write the unit.

Diagram support

No compulsory diagram is needed, but a labelled wave can support identification of wavelength before using the formula.

How CBSE asks it

Numericals usually give two values and ask for the third, often with a unit conversion hidden in the question.

Avoid common mistakes

Common confusion

Students often forget to convert centimetres to metres before using v = fλ.

Common wrong answer

Wrong answer: λ = vf. This is wrong because from v = fλ, wavelength is speed divided by frequency.

Exam tip

Write the formula first, substitute with units, and check whether the final unit is m/s, Hz, or m.

Quick check

A sound wave has frequency 200 Hz and wavelength 1.5 m. What is its speed?

The speed is 300 m/s because v = fλ = 200 × 1.5 = 300 m/s.

Study the wave speed relation v = fλ diagram carefully

Use the labelled diagram to keep wave speed relation v = fλ clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of wave speed relation v = fλ in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on wave speed relation v = fλ.

Revision cue

Revise wave speed relation v = fλ through the labels before writing the answer.

Answer writing and exam use

1-mark answer

The wave speed relation states that speed of a wave equals frequency multiplied by wavelength, written as v = fλ.

2-mark answer

The wave speed relation states that speed of a wave equals frequency multiplied by wavelength, written as v = fλ. v = fλ, where v is speed in m/s, f is frequency in Hz, and λ is wavelength in m. If sound has frequency 170 Hz and wavelength 2 m, its speed is v = 170 × 2 = 340 m/s.

3-mark answer

In the formula v = fλ, v is wave speed in metre per second, f is frequency in hertz, and λ is wavelength in metre. It is used when any two of speed, frequency, and wavelength are given. Correct unit conversion is important, especially when wavelength is given in centimetres. v = fλ, where v is speed in m/s, f is frequency in Hz, and λ is wavelength in m. A wave has speed 330 m/s and frequency 110 Hz. Using v = fλ, λ = v/f = 330/110 = 3 m. Numericals usually give two values and ask for the third, often with a unit conversion hidden in the question. Wrong answer: λ = vf. This is wrong because from v = fλ, wavelength is speed divided by frequency.
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