The distance between two successive crests of a wave is 15cm and the velocity 300$ms^{-1}$. Calculate the frequency.

1. Analyze the question

• Given: • Distance between two successive crests (Wavelength, $\lambda$) = $15\text{ cm}$ • Velocity ($v$) = $300\text{ ms}^{-1}$
• To find: Frequency ($f$)

2. Explain the concept

In wave motion, the distance between two successive crests is defined as the wavelength ($\lambda$). The relationship between velocity, frequency, and wavelength is given by the wave equation:

Where:

• $v$ is the velocity in meters per second ($\text{ms}^{-1}$)
• $f$ is the frequency in Hertz ($\text{Hz}$)
• $\lambda$ is the wavelength in meters ($\text{m}$)

Important Note: Always ensure your units are consistent. Since velocity is in $\text{ms}^{-1}$, the wavelength must be converted from centimeters to meters.

3. Show the solution

Step 1: Convert wavelength to meters

Step 2: Rearrange the wave equation to solve for frequency ($f$)

Step 3: Substitute the values

Step 4: Calculate the result To make the division easier, multiply both numerator and denominator by 100:

Step 5: Express in standard form

4. Identify the answer

Comparing our result to the given options, we find that $2.0 \times 10^3\text{ Hz}$ corresponds to option C.

5. Tip

Always check your units first! Many JAMB candidates lose marks because they forget to convert centimeters to meters. A quick way to remember: if the velocity is in meters, your wavelength must be in meters.