Calculating Wave Wavelength
To find the wavelength of the waves transmitted by the broadcasting station, we use the fundamental wave equation that relates speed, frequency, and wavelength.
Wave Equation
The relationship between the speed of a wave ($v$), its frequency ($f$), and its wavelength ($\lambda$) is given by the formula:
$ v = f \lambda $
Solving for Wavelength
We need to rearrange the formula to solve for the wavelength ($\lambda$):
$ \lambda = \frac{v}{f} $
Given Values
- Frequency ($f$): $71 \times 10^4\ Hz$
- Speed ($v$): $3 \times 10^8\ m/s$
Calculation Steps
- Substitute the given values into the rearranged formula:
$ \lambda = \frac{3 \times 10^8\ m/s}{71 \times 10^4\ Hz} $
- Simplify the expression:
$ \lambda = \frac{3}{71} \times \frac{10^8}{10^4}\ m $
$ \lambda = \frac{3}{71} \times 10^{(8-4)}\ m $
$ \lambda = \frac{3}{71} \times 10^4\ m $
- Calculate the numerical value:
$ \lambda \approx 0.0422535 \times 10^4\ m $
$ \lambda \approx 422.535\ m $
- Round the result to match the options provided (one decimal place):
$ \lambda \approx 422.5\ m $
Conclusion
The calculated wavelength of the wave is approximately $422.5\ m$. This corresponds to Option C.
Similar Questions
- A sound wave has a frequency of 4 kHz and a wavelength of 25 cm. How much time will it take to travel a distance of 2.5 km?
- In a longitudinal wave, the distance between two consecutive compressions and two consecutive rarefactions is called:
- If the frequency of a sound wave increases and the speed remains constant, its wavelength will:
Important Questions from Waves
Which of the following is related to Doppler effect?
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