1. Understanding the Concepts

* Frequency: The number of complete vibrations (or cycles) per second.

* Period: The time it takes for one complete vibration.

* Amplitude: The maximum displacement of the wave from its equilibrium position.

* Wavelength: The distance between two consecutive crests (or troughs) of the wave.

2. Calculating the Frequency

* The oscillator completes 40 vibrations in 30 seconds.

* Frequency (f) = Number of vibrations / Time = 40 / 30 = 4/3 Hz

3. Calculating the Speed

* We are given that the wave travels 425 cm in 10 seconds.

* Speed (v) = Distance / Time = 425 cm / 10 s = 42.5 cm/s

4. Using the Wave Equation

* The relationship between speed (v), frequency (f), and wavelength (λ) is:

* v = fλ

5. Solving for Wavelength

* We know v = 42.5 cm/s and f = 4/3 Hz

* Rearranging the equation: λ = v / f

* Substituting the values: λ = 42.5 cm/s / (4/3 Hz) = 31.875 cm

Therefore, the wavelength of the sinusoidal wave is 31.875 cm.