I'm quite sure there is no emergency vehicle anywhere within which you can travel 300 feet.
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Excellent question! It appears you're trying to connect the frequency of a wave to its velocity through the medium in which it's traveling, and you'll need to uncouple them. Let's look at some things to help you do that. If you've stood alongside a roadway and watched (and listened to) cars coming at you, you notice the pitch is higher as the vehicles approach, then lower as they pass and move away. The air is not moving toward you (unless you are way too close), and the sound is not coming at you "faster" and then "slower". The sound is traveling through the air at the same rate no matter which way the vehicle is moving. Here's what's happening. Sound comes from the source in the form of waves, moving out like an expanding bubble. When the vehicle is coming toward you rapidly, the vehicle shortens the gap between the siren and the next wave. The gap shortens because the sound only travels so fast and no faster, but the vehicle is catching up a little before the next wave comes out. This keeps happening, and if you could see the waves, you would see them bunching up together. The waves are closer. This means that there are more waves in one second's worth of sound. The frequency of sound waves is what gives rise to our experience of pitch. Higher frequency equals higher pitch. You can see what happens when the vehicle recedes. The sound is still traveling at the speed of sound, but because the vehicle is moving away, this has the effect of putting more space in between the waves of sound. there are fewer waves per second as the vehicle moves away from you; the sound hasn't changed velocity. Lower frequency equals lower pitch. It is essentially the same with light. Light, of course, does not need air or any other substance to travel through as sound does. But the light is not speeding up or slowing down. You are seeing either the "bunching up" of light waves or the "thinning" of the waves, depending on which way the object is moving. Think about it this way too. When you see light of various colors around you, you aren't imagining the different colors coming at you at different velocities, right? They all travel at the speed of light.
fear, panic, anxiety, fright, apprehension, nervousness, consternation, danger signal, warning, bell, alert, siren, hooter, distress signal