A vibrator generates the waves of the speed 330 m/s and wavelength 0 . 8 m. Then the frequency and time period are

Options

A. 264 Hz, 0 . 00 37 s
B. 42 . 5 Hz, 0 . 00 24 s
C. 412. 5 Hz, 0 . 00 24 s
D. 264 Hz, 0 . 00 30 s

Explanation

To solve the problem, we need to find the frequency and time period of the waves generated by the vibrator. We are given the speed of the wave (V) and the wavelength (λ). Let's go through the solution step by step.

### Step 1: Write down the given data
- Wave speed (V) = 330 m/s
- Wavelength (λ) = 0.8 m

### Step 2: Use the wave speed formula
The relationship between wave speed (V), frequency (ν), and wavelength (λ) is given by the formula:
\[ V = ν \cdot λ \]

### Step 3: Rearrange the formula to solve for frequency (ν)
To find the frequency, we can rearrange the formula:
\[ ν = \frac{V}{λ} \]

### Step 4: Substitute the values into the formula
Now substitute the known values into the formula:
\[ ν = \frac{330 \, \text{m/s}}{0.8 \, \text{m}} \]

### Step 5: Calculate the frequency
Perform the calculation:
\[ ν = \frac{330}{0.8} = 412.5 \, \text{Hz} \]

### Step 6: Find the time period (T)
The time period (T) is the reciprocal of the frequency (ν):
\[ T = \frac{1}{ν} \]

### Step 7: Substitute the frequency into the time period formula
Now substitute the frequency we calculated:
\[ T = \frac{1}{412.5 \, \text{Hz}} \]

### Step 8: Calculate the time period
Perform the calculation:
\[ T = 0.0024 \, \text{s} \]

### Final Answer
- Frequency (ν) = 412.5 Hz
- Time Period (T) = 0.0024 s

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