Question
A sound wave has a frequency of 440 Hz and is traveling at 343 m/s through air. Your classmate claims the wavelength is 1.5x105 m. Is your classmate correct? Why or why not? If not, give the correct wavelength.
Answers
Answered by
GPT-4o mini
To find the wavelength of a sound wave, you can use the wave equation, which relates the speed (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)):
\[
v = f \cdot \lambda
\]
We can rearrange this equation to solve for the wavelength:
\[
\lambda = \frac{v}{f}
\]
Given:
- Frequency (\(f\)) = 440 Hz
- Speed of sound (\(v\)) = 343 m/s
Now, we can substitute the values into the equation to find the wavelength:
\[
\lambda = \frac{343 \, \text{m/s}}{440 \, \text{Hz}}
\]
Calculating this gives:
\[
\lambda = \frac{343}{440} \approx 0.780 \, \text{m}
\]
This means the wavelength is approximately 0.780 meters, or 78.0 centimeters.
Your classmate is incorrect; the wavelength of the sound wave is not 1.5 × 10^5 meters. The correct wavelength is approximately 0.780 meters.
\[
v = f \cdot \lambda
\]
We can rearrange this equation to solve for the wavelength:
\[
\lambda = \frac{v}{f}
\]
Given:
- Frequency (\(f\)) = 440 Hz
- Speed of sound (\(v\)) = 343 m/s
Now, we can substitute the values into the equation to find the wavelength:
\[
\lambda = \frac{343 \, \text{m/s}}{440 \, \text{Hz}}
\]
Calculating this gives:
\[
\lambda = \frac{343}{440} \approx 0.780 \, \text{m}
\]
This means the wavelength is approximately 0.780 meters, or 78.0 centimeters.
Your classmate is incorrect; the wavelength of the sound wave is not 1.5 × 10^5 meters. The correct wavelength is approximately 0.780 meters.