Question

A plane progressive wave is given by y = 2 cos 2pi (330t - x) m. The frequency of the wave is:} 
 

• A. 165 Hz
• B. 330 Hz
• C. 660 Hz
• D. 340 Hz

Hint:

In the wave equation \( y = A \cos 2\pi (ft - \frac{x}{\lambda}) \), \( f \) represents the frequency of the wave.

Answer 1

The Correct Option is B

Step 1: {Identifying the frequency from the wave equation}
The general form of a plane progressive wave is: \[ y = A \cos 2\pi (ft - \frac{x}{\lambda}) \] Comparing with the given equation: \[ y = 2 \cos 2\pi (330t - x) \] The frequency \( f \) is 330 Hz.

Answer 2

Step 1: Understand the general wave equation
The standard form of a plane progressive wave is:
\[ y = A \cos 2\pi (ft - x/\lambda) \]
where:
- \( A \) is the amplitude
- \( f \) is the frequency
- \( \lambda \) is the wavelength

Step 2: Compare given wave equation
Given: \( y = 2 \cos 2\pi (330t - x) \)
This matches the standard form:
\[ y = A \cos 2\pi (ft - x/\lambda) \Rightarrow f = 330\, \text{Hz} \]

Step 3: Interpret the result
The term inside the cosine shows the frequency directly as the coefficient of \( t \) in the expression \( 2\pi(ft - x/\lambda) \).

Final Answer: 330 Hz