Sound traveling in air at 23$^{\circ}$C enters a cold front where the air temperature is 2$^{\circ}$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?
A) 0.009 m
B) 0.019 m
C) 0.067 m
D) 0.058 m

Question

Quizplus · Accepted Answer

The speed of sound in air is given by v = 331 m/s + 0.6 m/s/°C * T, where T is the temperature in °C. So, the speed of sound in the warm air is v_warm = 331 m/s + 0.6 m/s/°C * 23°C = 349 m/s, and the speed of sound in the cold air is v_cold = 331 m/s + 0.6 m/s/°C * 2°C = 333 m/s. The wavelength of a sound wave is given by λ = v/f, where v is the speed of sound and f is the frequency. So, the wavelength of the sound wave in the warm air is λ_warm = v_warm/f = 349 m/s / 1500 Hz = 0.233 m, and the wavelength of the sound wave in the cold air is λ_cold = v_cold/f = 333 m/s / 1500 Hz = 0.224 m. The difference in the wavelength between the cold air and the warm air is λ_cold - λ_warm = 0.224 m - 0.233 m = -0.009 m.

Sound Traveling in Air at 23 ∘^{\circ}∘ C Enters a Cold Front Where the Air Temperature Is

Sound Traveling in Air at 23 $^{\circ}$ C Enters a Cold Front Where the Air Temperature Is