Calculate the wavelength of sounds with frequencies 20 Hz and 20,000 Hz, given the speed of sound in air is 343 meters per second.

Steps to Solve

1. Calculate Wavelength for 20 Hz

To find the wavelength for the frequency of 20 Hz, we use the formula:

$$ \text{wavelength} = \frac{\text{speed of sound}}{\text{frequency}} $$

Substituting the values we have:

$$ \text{wavelength}_{20 \text{Hz}} = \frac{343 \text{ m/s}}{20 \text{ Hz}} $$

Perform the calculation:

$$ \text{wavelength}_{20 \text{Hz}} = 17.15 \text{ meters} $$

2. Calculate Wavelength for 20,000 Hz

Next, we calculate the wavelength for the frequency of 20,000 Hz using the same formula:

$$ \text{wavelength}_{20,000 \text{Hz}} = \frac{\text{speed of sound}}{\text{frequency}} $$

Substituting the values:

$$ \text{wavelength}_{20,000 \text{Hz}} = \frac{343 \text{ m/s}}{20,000 \text{ Hz}} $$

Performing the calculation gives:

$$ \text{wavelength}_{20,000 \text{Hz}} = 0.01715 \text{ meters} $$

3. Summarize Results

Now we have the wavelengths for both frequencies:

• For 20 Hz, the wavelength is approximately 17.15 meters.
• For 20,000 Hz, the wavelength is approximately 0.01715 meters.