The speed of wave of time period `T` and propagation constant `K` is

Options

A. `(2pi)/(TK)`
B. `(TK)/(2pi)`
C. `(1)/(TK)`
D. `(T)/(K)`

Explanation

To find the speed of a wave given its time period \( T \) and propagation constant \( k \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Wave Equation**:
The general equation of a wave can be expressed as:
\[ y = A \sin(\omega t - kx) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the propagation constant (also known as the wave number).

2. **Relate Angular Frequency to Time Period**:
The angular frequency \( \omega \) is related to the time period \( T \) by the formula:
\[ \omega = \frac{2\pi}{T} \]

3. **Formula for Wave Speed**:
The speed \( v \) of the wave can be calculated using the formula:
\[ v = \frac{\omega}{k} \]
where \( k \) is the propagation constant.

4. **Substitute \( \omega \) in the Speed Formula**:
Substitute the expression for \( \omega \) from step 2 into the speed formula:
\[ v = \frac{\frac{2\pi}{T}}{k} \]

5. **Simplify the Expression**:
This simplifies to:
\[ v = \frac{2\pi}{T} \cdot \frac{1}{k} = \frac{2\pi}{Tk} \]

6. **Final Result**:
Therefore, the speed of the wave in terms of its time period \( T \) and propagation constant \( k \) is:
\[ v = \frac{2\pi}{Tk} \]