The equation of a transverse wave is given by `y= 10sin2Π(2x-3t)` where x and y are in cm and t is in s. Its frequency is

Options

A. 1 Hz
B. 4 Hz
C. 2 Hz
D. 3 Hz

Answer

To find the frequency of the transverse wave given by the equation \( y = 10 \sin(2\pi(2x - 3t)) \), we can follow these steps:

1. **Identify the wave equation**: The given equation can be rewritten in a more recognizable form. The equation is \( y = 10 \sin(2\pi(2x - 3t)) \).

2. **Rewrite the equation**: We can express the equation as:
\[ y = 10 \sin(4\pi x - 6\pi t) \]
Here, we used the fact that \( 2\pi(2x - 3t) = 4\pi x - 6\pi t \).

3. **Identify the angular frequency (\( \omega \))**: In the standard wave equation \( y = a \sin(kx - \omega t) \), the term \( \omega \) represents the angular frequency. From our rewritten equation, we can see that:
\[ \omega = 6\pi \]

4. **Relate angular frequency to frequency**: The relationship between angular frequency (\( \omega \)) and frequency (\( f \)) is given by:
\[ \omega = 2\pi f \]
Substituting the value of \( \omega \):
\[ 6\pi = 2\pi f \]

5. **Solve for frequency (\( f \))**: To find \( f \), divide both sides of the equation by \( 2\pi \):
\[ f = \frac{6\pi}{2\pi} = 3 \]

Thus, the frequency of the wave is \( f = 3 \, \text{Hz} \).