Question

In the wave equation $ y = 3 \cos \pi (100t - x) \, \text{cm}$, the wavelength is

• A. 2 cm
• B. 3 cm
• C. 5 cm
• D. 100 cm

Hint:

To find the wavelength from the wave equation, use the wave number \( k \) and apply the formula \( \lambda = \frac{2\pi}{k} \).

Answer 1

The Correct Option is A

Step 1: Understanding the wave equation.
The given wave equation is:
\[ y = 3 \cos \pi (100t - x) \] This is a standard wave equation of the form: \[ y = A \cos(kx - \omega t) \] where \( k \) is the wave number and \( \omega \) is the angular frequency. 
Step 2: Identifying the wavelength.
In the equation \( y = 3 \cos \pi (100t - x) \), comparing it with the standard form, we see that \( k = \pi \). The relationship between the wave number \( k \) and the wavelength \( \lambda \) is: \[ k = \frac{2\pi}{\lambda} \] Thus: \[ \pi = \frac{2\pi}{\lambda} \quad \Rightarrow \quad \lambda = 2 \, \text{cm} \] Thus, the correct answer is 
(A) 2 cm.