v = fλ = 500 × 0.6 = 300 m/s. Basic wave equation and its physical meaning.

A Wave Has Frequency 500 Hz and Wavelength 0.6 m — Find Speed

Question

A wave has a frequency of 500 Hz and a wavelength of 0.6 m. Find the speed of the wave.

Solution — Step by Step

The fundamental relationship connecting wave speed, frequency, and wavelength is:

v = f\lambda

where $v$ is wave speed (m/s), $f$ is frequency (Hz), and $\lambda$ is wavelength (m). This isn’t just a formula to memorize — it comes directly from the definition of these quantities.

Frequency tells us how many complete waves pass a point per second. Wavelength tells us the length of one complete wave. So in one second, the wave front travels a distance equal to $f$ waves × $\lambda$ metres per wave. That product is exactly the speed.

v = f\lambda = 500 \times 0.6

v = \mathbf{300 \text{ m/s}}

Hz = s⁻¹, and wavelength is in metres. So:

\text{Hz} \times \text{m} = \text{s}^{-1} \times \text{m} = \text{m/s}

Units work out correctly — always do this check in board exams. One mark is often awarded for units alone.

Why This Works

The wave equation $v = f\lambda$ is one of the most elegant results in physics because it holds for all wave types — sound, light, water waves, seismic waves. The speed depends on the medium (not the source), while frequency is set by the source. Wavelength then adjusts automatically so that $v = f\lambda$ is always satisfied.

For context: 300 m/s is very close to the speed of sound in air at room temperature (~343 m/s). This is a reasonable sanity check — a 500 Hz wave is well within the audible range, and 300 m/s is a physically plausible sound speed.

Alternative Method — Using Period

If you’re given the time period $T$ instead of frequency, recall that $f = \frac{1}{T}$ . The wave equation becomes:

v = \frac{\lambda}{T}

This form has a clean physical meaning: the wave travels exactly one wavelength in one time period. For this problem, $T = \frac{1}{500} = 0.002$ s, so:

v = \frac{0.6}{0.002} = 300 \text{ m/s}

Same answer, different route. In JEE Main, both forms appear in options — knowing both saves you from being tricked.

Common Mistake

Students sometimes confuse wavelength with amplitude, especially when a question describes a “tall wave.” Amplitude has nothing to do with speed or wavelength — it measures how much the medium is displaced, not how far apart the crests are. If you substitute amplitude into $v = f\lambda$ , your answer will be completely wrong and the units won’t even match.

300 m/s is a benchmark value worth remembering — speed of light is $3 \times 10^8$ m/s, speed of sound in air is ~340 m/s, and here we get 300 m/s for this wave. NCERT often picks numbers that give round answers. If your calculation gives something messy like 317.4, recheck your substitution.

Question

Solution — Step by Step

Why This Works

Alternative Method — Using Period

Common Mistake

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