Wave Speed, Frequency and Wavelength: What Stays Fixed in One Medium?

For a periodic travelling wave, v = fλ. When wave speed is fixed by the stated medium and conditions, a higher frequency means a shorter wavelength, not automatically a higher propagation speed.

Name the three quantities

Frequency counts cycles per second and is measured in hertz. Wavelength is the spatial distance between corresponding points in neighbouring cycles. Propagation speed describes how quickly the disturbance travels. They are related, but none is a substitute for the others.

One period is T = 1/f. During that time a repeating wave pattern moves one wavelength, giving v = λ/T = fλ. This short derivation explains why the units work: (1/s) × m = m/s. The oscillation of a particle in the medium is a different motion from propagation of the pattern.

Worked example

A wave model has propagation speed 24 m/s and frequency 6 Hz. Its wavelength is λ = v/f = 24/6 = 4 m. The period is 1/6 s. A pattern travelling 4 m in 1/6 s indeed has speed 24 m/s.

Now change the source to 8 Hz while the exercise keeps the propagation speed at 24 m/s. The wavelength becomes 24/8 = 3 m. The frequency ratio is 8/6, while the wavelength ratio is 3/4, its reciprocal. Multiplying the new frequency and wavelength still gives the stated speed.

Check the physical assumption

A fixed speed is an assumption about the wave and medium in the problem. Some waves are dispersive, and their speed can depend on frequency. Do not turn an introductory constant-speed model into a universal claim for every water, sound or light wave.

At a stationary boundary in a simple transmission problem, the source frequency can stay the same while speed and wavelength change in the new medium. The equation still applies on each side with the local speed. State which medium your numbers describe.

Common mistake

Convert kilohertz to hertz and centimetres to metres before calculating. Amplitude is not wavelength: increasing the height of a small-amplitude wave does not mean that more cycles pass per second. Label frequency, wavelength, speed and any fixed-medium condition before rearranging the equation.

Same speed ho to frequency badhegi, wavelength ghategi—dono ko same mat samjho.

Three practice questions with worked answers

1. A wave has f = 5 Hz and λ = 2 m. Find speed.

   v = fλ = 5 × 2 = 10 m/s.

2. Speed is 300 m/s and frequency is 1.5 kHz. Find wavelength.

   1.5 kHz = 1,500 Hz. λ = 300/1,500 = 0.20 m.

3. At fixed speed, frequency doubles. What happens to wavelength?

   Since λ = v/f, wavelength becomes half its original value.

Related study guides

• Sound Class 9 Notes: Wave Terms, Speed, Echo and Ultrasound Numericals
• Waves and Oscillations for JEE: SHM Formulas, Springs, Pendulum and Wave Equation

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References and authorship

Original examples and practice questions, prepared with AI assistance and editorial arithmetic review. Related definitions and methods: OpenStax: Waves. No textbook or exam-board affiliation is claimed.