The equation of a sound wave is `y=0.0015sin(62.4x+316t)` the wavelength of this wave is

Options

A. `0.2 unit`
B. `0.1 unit`
C. `0.3 unit`
D. cannot the calcualted

Explanation

To find the wavelength of the sound wave given by the equation \( y = 0.0015 \sin(62.4x + 316t) \), we can follow these steps:

### Step 1: Identify the wave equation format
The general form of a wave equation is:
\[ y = a \sin(kx + \omega t) \]
where:
- \( a \) is the amplitude,
- \( k \) is the wave number,
- \( \omega \) is the angular frequency.

### Step 2: Extract the wave number \( k \)
From the given equation \( y = 0.0015 \sin(62.4x + 316t) \), we can see that:
\[ k = 62.4 \]

### Step 3: Relate wave number \( k \) to wavelength \( \lambda \)
The wave number \( k \) is related to the wavelength \( \lambda \) by the formula:
\[ k = \frac{2\pi}{\lambda} \]

### Step 4: Rearrange the formula to find \( \lambda \)
To find the wavelength \( \lambda \), we can rearrange the formula:
\[ \lambda = \frac{2\pi}{k} \]

### Step 5: Substitute the value of \( k \)
Now, substitute the value of \( k \):
\[ \lambda = \frac{2\pi}{62.4} \]

### Step 6: Calculate the wavelength
Now, we can calculate \( \lambda \):
\[ \lambda = \frac{2 \times 3.14159}{62.4} \approx \frac{6.28318}{62.4} \approx 0.1007 \]

### Step 7: Round to appropriate significant figures
Rounding to three significant figures, we get:
\[ \lambda \approx 0.1 \text{ m} \]

Thus, the wavelength of the wave is approximately \( 0.1 \) meters.

### Final Answer
The wavelength of the sound wave is \( \lambda \approx 0.1 \, \text{m} \).

---