Question

Calculate the wavelength of a guitar string that produces a note with a frequency of 440 Hz, assuming the speed of sound in air is 343 meters per second.

Answer 1

To calculate the wavelength of a sound wave produced by a guitar string, we can use the formula:

\[
\text{Wavelength} (\lambda) = \frac{\text{Speed of Sound} (v)}{\text{Frequency} (f)}
\]

Given:
- Speed of sound in air, \( v = 343 \, \text{m/s} \)
- Frequency of the note, \( f = 440 \, \text{Hz} \)

Now we substitute the values into the formula:

\[
\lambda = \frac{343 \, \text{m/s}}{440 \, \text{Hz}}
\]

Calculating this gives:

\[
\lambda = \frac{343}{440} \approx 0.780 \, \text{meters}
\]

Thus, the wavelength of the sound produced by the guitar string is approximately **0.780 meters**.