Write down the equation of a wave travelling in the negative direaction along x-axis with an amplitude `0.01 m`, a frequency `550 Hz` and a speed `330 m//s`.

Answer

To write down the equation of a wave traveling in the negative direction along the x-axis with the given parameters, we will follow these steps:

### Step 1: Identify the parameters
- Amplitude (A) = 0.01 m
- Frequency (f) = 550 Hz
- Speed (v) = 330 m/s

### Step 2: Calculate the wavelength (λ)
The wavelength can be calculated using the formula:
\[ \lambda = \frac{v}{f} \]
Substituting the values:
\[ \lambda = \frac{330 \, \text{m/s}}{550 \, \text{Hz}} = \frac{330}{550} = \frac{3}{5} \, \text{m} \]

### Step 3: Calculate angular frequency (ω) and wave number (k)
- Angular frequency (ω) is given by:
\[ \omega = 2\pi f \]
Substituting the frequency:
\[ \omega = 2\pi \times 550 = 1100\pi \, \text{rad/s} \]

- Wave number (k) is given by:
\[ k = \frac{2\pi}{\lambda} \]
Substituting the wavelength:
\[ k = \frac{2\pi}{\frac{3}{5}} = \frac{2\pi \times 5}{3} = \frac{10\pi}{3} \, \text{rad/m} \]

### Step 4: Write the wave equation
For a wave traveling in the negative x-direction, the general form of the wave equation is:
\[ y = A \sin(\omega t + kx) \]
Substituting the values of A, ω, and k:
\[ y = 0.01 \sin(1100\pi t + \frac{10\pi}{3} x) \]

### Final Wave Equation
Thus, the equation of the wave traveling in the negative direction along the x-axis is:
\[ y = 0.01 \sin(1100\pi t + \frac{10\pi}{3} x) \]

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