Question

speed of sound in air is directly proportional to square root of absolute temperature of air (keeping other parameters constant). the speed of sound in air at 273k and 1 atom is 332 m/s. on a clear day, when temperature in the laboratory was 27o c, an experiment was performed to measure speed of sound in air in the laboratory. the measured value comes out to be 352 m/s. the percentage error in this measurement is

Answer 1

The speed of sound in air is related to temperature, and by applying the relationship between speed and square root of absolute temperature, we calculate the expected speed of sound at 300 K and compare it to the measured value to get the percentage error.

Step-by-step explanation:

The speed of sound in air is directly proportional to the square root of the absolute temperature of the air. Given the speed of sound at 273 K is 332 m/s, we can find the expected speed of sound at 27°C (which is 300 K) using the ratio of square roots of the absolute temperatures:

Expected speed at 300 K = 332 m/s × sqrt(300/273)

Once we calculate the expected speed, we can determine the percentage error by comparing it to the measured value of 352 m/s:

Percentage error = |(Measured speed - Expected speed) / Expected speed| × 100%

Using the data given, we would see that the percentage error in the measurement of the speed of sound on this clear day in the laboratory is relatively small, indicating the measurement is fairly precise.