To determine the speed of sound given a frequency and a wavelength, we can use the relationship from the wave equation:
[tex]\[ \text{Speed of Sound} = \text{Frequency} \times \text{Wavelength} \][/tex]
Let's break down the steps:
1. Identify the given values:
- Frequency ([tex]\(f\)[/tex]) = 266 Hz
- Wavelength ([tex]\(\lambda\)[/tex]) = 1.3 m
2. Apply the relationship:
Substitute the given values into the formula:
[tex]\[
\text{Speed of Sound} = 266 \text{ Hz} \times 1.3 \text{ meters}
\][/tex]
3. Calculate the Speed of Sound:
Perform the multiplication:
[tex]\[
\text{Speed of Sound} = 266 \times 1.3 = 345.8 \, \text{m/s}
\][/tex]
Therefore, the speed of sound, when the frequency is 266 Hz and the wavelength is 1.3 meters, is [tex]\(345.8 \, \text{m/s}\)[/tex].
From the given options:
- [tex]$102 \, \text{m/s}$[/tex]
- [tex]$346 \, \text{m/s}$[/tex]
- [tex]$692 \, \text{m/s}$[/tex]
The closest value to our calculated speed of sound is [tex]\(346 \, \text{m/s}\)[/tex]. So, the correct answer is:
[tex]\[ \boxed{346 \, \text{m/s}} \][/tex]
