A wave is described by the equation $y=0.05\ast \sin (2\pi x/0.4)$ where $y$ and $x$ are in meters. What are the amplitude and wavelength of this wave?

• A. Amplitude: $0.05$ m, Wavelength: $0.4$ m
• B. Amplitude: $0.4$ m, Wavelength: $0.05$ m
• C. Amplitude: $0.05$ m, Wavelength: $2$ m
• D. Amplitude: $2$ m, Wavelength: $0.4$ m

Answer: (A)

Verified step by step guidance

1. Identify the general form of the wave equation, which is typically written as \(y = A \sin\left(\frac{2\pi}{\lambda} x\right)\), where \(A\) is the amplitude and \(\lambda\) is the wavelength.
2. Compare the given wave equation \(y = 0.05 \sin\left(\frac{2\pi}{0.4} x\right)\) to the general form to determine the amplitude and the wavelength.
3. From the equation, recognize that the coefficient in front of the sine function, \$0.05\(, represents the amplitude \)A$ of the wave.
4. The term inside the sine function is \(\frac{2\pi}{0.4} x\), which matches the form \(\frac{2\pi}{\lambda} x\), so the wavelength \(\lambda\) is \$0.4$ meters.
5. Summarize the results: amplitude \(A = 0.05\) m and wavelength \(\lambda = 0.4\) m.