Question

$y = 3 \cos 100 \pi (2 t - x)$. The value of $\lambda$ is

• A. 4 cm
• B. 6 cm
• C. 2 cm
• D. 1 cm

Answer 1

Answer: (C)

2 cm

Answer 2

The given wave equation is

$y = 3 \cos\Bigl(100\pi (2t - x)\Bigr)$.

Expanding the argument, we have:

$y = 3 \cos \Bigl(200\pi t - 100\pi x\Bigr)$.

Comparing with the standard form

$y = A \cos(\omega t - kx)$,

we identify:

$\omega = 200\pi \quad \text{and} \quad k = 100\pi$.

The wavelength is given by:

$\lambda = \frac{2\pi}{k} = \frac{2\pi}{100\pi} = \frac{2}{100} = \frac{1}{50} \text{ m}$.

Since 1 m = 100 cm,

$\lambda = \frac{1}{50} \text{ m} = \frac{100}{50} \text{ cm} = 2 \text{ cm}$.