Sound traveling in air at 23^°C enters a cold front where the air temperature is 2^°C. If the frequency of the sound is 1500 Hz, what is the difference in the wavelength between the cold air and the warm air? The speed of sound in air at 20^°C is 343 m/s. A) 8.3 mm B) 9.0 mm C) 1.9 cm D) 6.7 cm

Question

Quizplus · Accepted Answer

The speed of sound in air increases with temperature. At 20°C, the speed is 343 m/s. For every degree Celsius, the speed of sound in air changes by approximately 0.6 m/s. Thus, at 25°C, the speed is 343 + (5*0.6) = 346 m/s, and at 2°C, it is 343 - (18*0.6) = 331.2 m/s. The wavelength ($\lambda$) is given by $\lambda = v/f$, where $v$ is the speed of sound and $f$ is the frequency. The difference in wavelength ($\Delta\lambda$) between the cold and warm air is $\Delta\lambda = \lambda_{warm} - \lambda_{cold} = (346/1500) - (331.2/1500)$. This calculation results in a difference of approximately 0.0083 meters, or 8.3 mm.

Sound Traveling in Air at 23°C Enters a Cold Front

Sound Traveling in Air at 23^°C Enters a Cold Front