A vibrator causes water ripples to travel across the surface of a tank. The wave travels 50cm in 2s and the…

1. Analyze the Question

We are given:

• Distance ($d$): 50 cm
• Time ($t$): 2 s
• Wavelength ($\lambda$): 5 cm (the distance between successive crests)
• Goal: Calculate the frequency ($f$) of the vibrator.

2. Explain the Concept

To solve this, we use two fundamental wave equations:

1. Wave Speed ($v$): Speed is the total distance covered divided by the time taken. $$v = \frac{d}{t}$$
2. Wave Equation: The relationship between speed, frequency, and wavelength is: $$v = f \times \lambda$$Rearranging this to find frequency, we get:$$f = \frac{v}{\lambda}$$

3. Show the Solution

Step 1: Calculate the speed of the wave ($v$).

Step 2: Calculate the frequency ($f$). Using the wave equation $v = f \times \lambda$:

4. Identify the Answer

The frequency of the vibrator is 5 Hz. Comparing this to the given options, the correct choice is A.

5. Exam Tip

In wave problems, always check your units. Since the distance and wavelength were both in centimeters (cm), you didn't need to convert to meters, as the units canceled out. However, if the speed was asked for in m/s, you would have needed to convert the distance to meters first. Always keep an eye on those units!