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

Options

A. 0.4 unit
B. 0.3 unit
C. 0.2 unit
D. 0.1 unit

Answer

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 number \( k \)
The general form of a wave equation is given by:
\[ y = A \sin(kx + \omega t) \]
where \( k \) is the wave number. From the given equation, we can see that:
\[ k = 62.4 \, \text{(from the equation)} \]

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

### Step 3: Rearrange the formula to find wavelength
We can rearrange the formula to solve for \( \lambda \):
\[ \lambda = \frac{2\pi}{k} \]

### Step 4: Substitute the value of \( k \)
Now we substitute the value of \( k \) into the equation:
\[ \lambda = \frac{2\pi}{62.4} \]

### Step 5: Calculate the wavelength
Using \( \pi \approx 3.14 \):
\[ \lambda = \frac{2 \times 3.14}{62.4} \approx \frac{6.28}{62.4} \approx 0.1005 \, \text{meters} \]

### Step 6: Round the answer
Rounding to two decimal places, we get:
\[ \lambda \approx 0.1 \, \text{meters} \]

Thus, the wavelength of the wave is approximately \( 0.1 \, \text{m} \).

### Final Answer
The wavelength \( \lambda \) is \( 0.1 \, \text{m} \).

---