Question

What is the wavelength for a wave having frequency 50 Hz?

• A. $1.6 \times 10^6\ \text{m}$
• B. $6 \times 10^{-2}\ \text{m}$
• C. $6 \times 10^6\ \text{m}$
• D. $15 \times 10^2\ \text{m}$

Hint:

When dividing a number by 50, a fast mental math trick is to multiply the numerator by 2 and shift the decimal place two slots to the left (since dividing by 50 is equivalent to multiplying by $\frac{2}{100}$).
Here, $3 \times 2 = 6$. Adjusting the exponents directly gives $6 \times 10^6$ with zero manual long division!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem requires finding the wavelength ($\lambda$) of an electromagnetic wave given its vibrational frequency ($\nu = 50\ \text{Hz}$).

Step 2: Key Formula or Approach:
The fundamental relationship connecting the speed, frequency, and wavelength of an electromagnetic wave is governed by the wave equation:
$$c = \nu \lambda$$
Where:
$c = $ Speed of light in a vacuum or air $\approx 3 \times 10^8\ \text{m/s}$
$\nu = $ Frequency of the wave in Hz ($\text{s}^{-1}$)
$\lambda = $ Wavelength of the wave in meters (m)
Rearranging the equation to solve for wavelength gives:
$$\lambda = \frac{c}{\nu}$$

Step 3: Detailed Explanation:
Substitute the given physical constants and values into our rearranged equation:
$$\lambda = \frac{3 \times 10^8\ \text{m/s}}{50\ \text{s}^{-1}}$$
To simplify the division, we can rewrite $3 \times 10^8$ as $300 \times 10^6$:
$$\lambda = \frac{300 \times 10^6}{50} = 6 \times 10^6\ \text{m}$$

Step 4: Final Answer:
The wavelength of the wave is $6 \times 10^6\ \text{m}$, which matches option (C).