Time period of a wave is `5xx10^(-3)s,` what is the frequency?

Options

A. `5xx10^(-3)s^(-1)`
B. `2xx10^(2)s^(-1)`
C. `23xx10^(3)s^(-1)`
D. `5xx10^(2)s^(-1)`

Explanation

To find the frequency of a wave when given its time period, we can use the relationship between frequency (f) and time period (T). The formula is:

\[ f = \frac{1}{T} \]

### Step-by-step Solution:

1. **Identify the time period (T)**:
The time period given in the question is \( T = 5 \times 10^{-3} \) seconds.

2. **Apply the formula for frequency**:
Substitute the value of the time period into the formula:
\[ f = \frac{1}{T} = \frac{1}{5 \times 10^{-3}} \]

3. **Simplify the expression**:
To simplify \( \frac{1}{5 \times 10^{-3}} \), we can rewrite it as:
\[ f = \frac{1}{5} \times \frac{1}{10^{-3}} = \frac{1}{5} \times 10^{3} \]

4. **Calculate the frequency**:
Now, calculate \( \frac{1}{5} \):
\[ \frac{1}{5} = 0.2 \]
Therefore,
\[ f = 0.2 \times 10^{3} = 200 \text{ Hz} \]

5. **Express in scientific notation**:
To express 200 in scientific notation:
\[ 200 = 2 \times 10^{2} \text{ Hz} \]

Thus, the frequency of the wave is \( 2 \times 10^{2} \text{ Hz} \).

### Final Answer:
The frequency of the wave is \( 2 \times 10^{2} \text{ Hz} \).

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