What is the effect of a cold?

Doppler effect on a cold or hot day?

• This question comes out of my 1001 questions for mcat physics and is dealing with the Doppler effect on a warm or cold day The question states: Sound moves faster on a warm day than on a cold day. The Doppler effect will be greater on which day? Now, in the question stem, it simply states, "Sound moves faster on a warm day than on a cold day" and I'm assuming this has to do with the gas molecules increasing collisions due to temperature. So I would expect the Doppler effect to be greater on a warm day. But the answer is: on a cold day because the velocities of the source and observer will be more significant compared to the velocity of sound. Can someone please explain this concept to me before I waste another hour battling science concepts and going nuts? haha. Thanks in advance!

• Answer:

  It means relative velocities will matter more on a cold day. Sound moves at roughly 340 metres per second, so if we lower that figure by slowing the sound down it gets closer to the speed of a car - about 25m/s driving along a road, say. So as the car moved past you the speed difference would be 50m/s. 330 is closer to 50 than 340. It is this difference that matters for the doppler effect. Say a car is moving toward you: If sound were going really really fast it wouldn't matter so much if the car were moving toward you or away - the waves would still be given off almost as close together as they arrive, and there would be very little change if the car goes past you and starts moving away. If sound were really slow the difference would be much bigger since the car would have moved a long way before the next crest of the sound wave was emitted, so the change in speed as the car went past (compared to the slow speed of sound) would make a much bigger difference to the frequency that arrives at your ear. This is what happens on a cold day.