ANSWER
[tex]8.66\text{ }m[/tex]
EXPLANATION
First, we have to find the frequency of the sound in the air.
To do this, apply the formula for the speed of a wave:
[tex]v=\lambda *f[/tex]
where λ = wavelength
f = frequency
The speed of sound in air is 332 m/s at 0 degrees Celsius.
Hence, using the formula given, the speed of sound in the air of 22 degrees Celsius is:
[tex]\begin{gathered} v=332+0.6*22=332+13.2 \\ v=345.2\text{ }m\/s \end{gathered}[/tex]
Therefore, the frequency of the sound is:
[tex]\begin{gathered} 345.2=0.785*f \\ f=\frac{345.2}{0.785} \\ f=439.75\text{ }Hz \end{gathered}[/tex]
Now, we can apply the formula for the speed of sound in marble to find the wavelength of the wave after it travels into the marble:
[tex]\begin{gathered} v=\lambda *f \\ \lambda=\frac{v}{f} \end{gathered}[/tex]
Note: the frequency of the sound in the air and marble are the same
Therefore, the wavelength of the wave after it travels into marble is:
[tex]\begin{gathered} \lambda=\frac{3810}{439.75} \\ \lambda=8.66\text{ }m \end{gathered}[/tex]
That is the wavelength of the wave after it travels into marble.
