The wavelength of a wave traveling with a velocity of 420 ms$^{-1}$ is 42 m. What is its period?

Analyze the question

You're given the wave speed (v = 420 m/s) and the wavelength (λ = 42 m), and you need the period (T).

Concept

The wave equation links these quantities:

v = fλ

The period is the reciprocal of the frequency:

T = 1/f

Combining the two gives T = λ/v.

Solution

1. Find the frequency: f = v/λ = 420 / 42 = 10 Hz

2. Find the period: T = 1/f = 1/10 = 0.1 s

Check using T = λ/v = 42/420 = 0.1 s ✓

Answer

The period is 0.1 s, which is option D.

Tip

When you see wavelength, velocity and period together, go straight to T = λ/v. Also remember that a larger frequency means a smaller period. A frequency of 10 Hz means 10 waves pass every second, so each takes 0.1 s.