On a 22.2°C day, you measure a sound wave to have a wavelength of 1.55 m and a frequency of 203.8 Hz. Determine the percent error of these measurements.

The speed of sound, which can be calculated by multiplying the given wavelength and frequency, is 316.03 m/s. The accepted value at 22.2 °C is approximately 343.7 m/s. Hence, the calculated percent error of these measurements is around 8.03%.

Explanation:

To calculate the speed of sound, we will multiply the wavelength (1.55 m) by the frequency (203.8 Hz). That gives us a result of 316.03 m/s. However, at 22.2 °C the speed of sound in air, based on empirical data, is approximately 343.7 m/s.

Percentage error is calculated using the formula: | Experimental Value - Accepted Value | / | Accepted Value | * 100%. In this case, our experimental value is 316.03 m/s and our accepted value is 343.7 m/s.

Using these values in the formula we get: |316.03 m/s - 343.7 m/s| / |343.7 m/s| * 100%. This gives us approximately 8.03 %. Therefore, the measurement has a percent error of 8.03%.

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