To determine the correct equation for the traveling wave described in the question, we need to analyze the parameters given: amplitude, frequency, and wavelength. ### Given Parameters: - **Amplitude (A)**: 0.15 m - **Frequency (f)**: 550 Hz - **Wavelength (λ)**: 0.01 m ### Step 1: Understanding Wave Equation The general form of a traveling wave can be expressed as: \[ y(x, t) = A \sin(kx - \omega t) \] where: - \( A \) is the amplitude, - \( k \) is the wave number, - \( \omega \) is the angular frequency, - \( x \) is the position, - \( t \) is the time. ### Step 2: Calculate Wave Number (k) and Angular Frequency (ω) 1. **Wave Number (k)**: The wave number \( k \) is given by the formula: \[ k = \frac{2\pi}{\lambda} \] Substituting the wavelength: \[ k = \frac{2\pi}{0.01} = 200\pi \, \text{m}^{-1} \] 2. **Angular Frequency (ω)**: The angular frequency \( \omega \) is given by: \[ \omega = 2\pi f \] Substituting the frequency: \[ \omega = 2\pi \times 550 = 1100\pi \, \text{rad/s} \] ### Step 3: Formulate the Wave Equation Now we can substitute the values of \( A \), \( k \), and \( \omega \) into the wave equation: \[ y(x, t) = 0.15 \sin(200\pi x - 1100\pi t) \] ### Step 4: Rearranging the Equation The equation can be rearranged to match the form in the options: \[ y = 0.15 \sin(200\pi (x - 5.5t)) \] This is because \( 1100\pi = 200\pi \times 5.5 \). ### Step 5: Identify the Correct Option Now, let's compare this derived equation with the options provided: - **Option A**: \( y = 0.15 \sin(200\pi(x - 5.5t)) \) - **This matches our derived equation.** - **Option B**: \( y = 0.15 \sin(\pi(0.01x - 5.5t)) \) - This does not match because the wave number and angular frequency are incorrect. - **Option C**: \( y = 0.15 \sin(5.5\pi(x - 200t)) \) - This is incorrect as the coefficients do not match the calculated values. - **Option D**: \( y = 0.15 \sin(\pi(550x - 0.01t)) \) - This is incorrect because the terms inside the sine function do not correspond to the correct wave number and angular frequency. ### Conclusion The correct option is **A**: \( y = 0.15 \sin(200\pi(x - 5.5t)) \). ### Revision Summary: - The wave equation is derived from amplitude, frequency, and wavelength. - Wave number \( k \) is calculated as \( k = \frac{2\pi}{\lambda} \). - Angular frequency \( \omega \) is calculated as \( \omega = 2\pi f \). - The correct wave equation matches the derived form, confirming option A as correct.