What is the wavelength for a wave having frequency 50 Hz?
Show 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!
Step 1: Read the question.
We are given a wave with frequency $\nu = 50\ \text{Hz}$ and asked for its wavelength $\lambda$.
Step 2: Recall the wave equation.
For an electromagnetic wave, speed equals frequency times wavelength:
\[ c = \nu \lambda \]
Step 3: Know the speed of light.
The speed $c$ is about $3 \times 10^8\ \text{m/s}$. This is fixed for such waves in air or vacuum.
Step 4: Rearrange for wavelength.
\[ \lambda = \frac{c}{\nu} \]
Step 5: Put in the values.
\[ \lambda = \frac{3 \times 10^8}{50} \]
To divide easily, write $3 \times 10^8$ as $300 \times 10^6$.
Step 6: Finish the division.
\[ \lambda = \frac{300 \times 10^6}{50} = 6 \times 10^6\ \text{m} \]
\[ \boxed{6 \times 10^6\ \text{m}} \]