A truck sounds its 810 hz horn as it drives outside a house at 30mph. But the occupant's ear detects a frequency of 780hz. What is the temperature of the air at this location?

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  1. According to the Doppler shift equation for a moving source,

    780 = 810*[a/(a + 30)]

    where a is the speed of sound.

    The truck must be receding from the observer since the shift is to a lower frequency.

    1 + (30/a) = 1.0385
    30/a = 0.0385
    a = 779 mph = 1254 km/h = 348 m/s

    Next, find the temperature that gives you that speed of sound in air. There are plenty of places online to do that.

    It will be a rather hot day.

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