1. **Purpose:** Calculate the speed of sound in air using the Doppler effect. 2. **Materials:** Electric skateboard, tone generator, GPS device, electric tuner. 3. **Apparatus:** GPS and tone generator on skateboard, electric tuner on ground. 4. **Method:** - Place GPS and tone generator on skateboard. - Place electric tuner on ground. - Turn on tone generator and record frequency at rest. - Move skateboard toward tuner at constant speed. - Record speed from GPS and observed frequency from tuner. 5. **Results:** - Frequency at rest $f_0 = 815.06$ Hz. - Speed of skateboard $v_s = 38.65$ m/s. - Observed frequency $f = 916.08$ Hz. 6. **Analysis:** - Use Doppler effect formula for approaching source: $$f = f_0 \frac{v}{v - v_s}$$ where $v$ is speed of sound. - Rearranged to solve for $v$: $$f = f_0 \frac{v}{v - v_s} \Rightarrow f(v - v_s) = f_0 v$$ $$fv - fv_s = f_0 v$$ $$fv - f_0 v = fv_s$$ $$v(f - f_0) = fv_s$$ $$v = \frac{f v_s}{f - f_0}$$ - Substitute values: $$v = \frac{916.08 \times 38.65}{916.08 - 815.06} = \frac{35388.132}{101.02}$$ - Calculate: $$v \approx 350.5 \text{ m/s}$$ - Theoretical speed of sound at 16.0 °C: $$v_{theoretical} = 331 + 0.6 \times 16 = 331 + 9.6 = 340.6 \text{ m/s}$$ - Percent error: $$\text{Percent error} = \left| \frac{350.5 - 340.6}{340.6} \right| \times 100 = 2.87\%$$ 7. **Conclusion:** - The experimentally measured speed of sound is approximately 350.5 m/s, which closely matches the theoretical value of 340.6 m/s at 16.0 °C. - Small percent error indicates good accuracy. - Possible errors include misalignment of skateboard and tuner affecting speed measurement and temperature variations affecting theoretical value. This completes the lab report for the speed of sound using the Doppler effect.