In the wave equation $ y = 3 \cos \pi (100t - x) \, \text{cm}$, the wavelength is
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- 2 cm
- 3 cm
- 5 cm
- 100 cm
The Correct Option is A
Solution and Explanation
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.
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