Let's walk through the solution step-by-step to find the difference in wavelength between the wave produced in ice and the wave produced in water.
Given:
- The frequency of the sound wave is 550 Hz.
- The speed of sound in ice is 3200 m/s.
- The speed of sound in water is 1500 m/s.
To find the wavelength, we use the formula:
[tex]\[ \lambda = \frac{v}{f} \][/tex]
where [tex]\( \lambda \)[/tex] is the wavelength, [tex]\( v \)[/tex] is the speed of sound, and [tex]\( f \)[/tex] is the frequency.
Step 1: Calculate the wavelength in ice
[tex]\[
\lambda_{\text{ice}} = \frac{3200 \text{ m/s}}{550 \text{ Hz}} \approx 5.818 \text{ m}
\][/tex]
Step 2: Calculate the wavelength in water
[tex]\[
\lambda_{\text{water}} = \frac{1500 \text{ m/s}}{550 \text{ Hz}} \approx 2.727 \text{ m}
\][/tex]
Step 3: Determine the difference in wavelength between ice and water
[tex]\[
\Delta \lambda = \lambda_{\text{ice}} - \lambda_{\text{water}} \approx 5.818 \text{ m} - 2.727 \text{ m} \approx 3.091 \text{ m}
\][/tex]
Thus, the difference in wavelength between the wave produced in ice and the wave produced in water is approximately 3.1 m. Hence, the correct answer is:
3.1 m
