Calculate wavelength given frequency.
Understand the Problem
The question is asking how to calculate the wavelength when the frequency is known. This involves using the formula that relates wavelength, frequency, and the speed of light (or sound) depending on the context.
Answer
$0.780 \, \text{m}$
Answer for screen readers
The wavelength is approximately $0.780 , \text{m}$.
Steps to Solve
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Identify the formula
To calculate the wavelength ($\lambda$), we use the formula:
$$ \lambda = \frac{v}{f} $$
where ( v ) is the speed of the wave and ( f ) is the frequency. -
Determine the values
Identify the values for the speed ( v ) and the frequency ( f ). Make sure they are in consistent units, usually meters per second (m/s) for speed, and hertz (Hz) for frequency. -
Substitute values into the formula
Plug in the known values into the wavelength formula. If, for example, ( v = 343 , \text{m/s} ) (speed of sound in air) and ( f = 440 , \text{Hz} ) (frequency of A4 note), we have:
$$ \lambda = \frac{343}{440} $$ -
Perform the calculation
Calculate the wavelength by dividing the speed by the frequency. Continuing with our example:
$$ \lambda = \frac{343}{440} \approx 0.780 , \text{m} $$ -
Result interpretation
Analyze the result, understanding that it represents the physical length of one wave cycle in meters.
The wavelength is approximately $0.780 , \text{m}$.
More Information
This result indicates that for a frequency of 440 Hz, the wavelength of the sound wave is about 0.780 meters. This frequency corresponds to the note A4, commonly used in music tuning.
Tips
- Using inconsistent units: Ensure speed and frequency are in compatible units (e.g., m/s and Hz).
- Forgetting to modify the formula: If calculating for different media (like sound in water), remember to use the correct speed.
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