Illustration of Doppler Effect Introduction There are multiple articles and videos available on the internet which explain the Doppler effect, mostly using the fact that the waves get compressed when an object making sound approaches you and that the waves are stretched when the object moves away from you. These explanations are good enough, but don’t provide a deeper understanding. Also derivation of the formula for frequency change is left to the reader. This post is an attempt to explain in a layman’s terms the effects on the frequency of sound we hear. Subsonic & Mach 1 speeds In all the examples below, it’s assumed that the police car (Well, considering the speeds in the examples, it would be more like a jet!) running the siren is 12 seconds away initially, it approaches and subsequently passes you. You stop hearing the sound once it gets 12 seconds away from you. Approaching car Case 1 - Cop car traveling at 1/4th the speed of sound The initial sound emitte...
It's tax planning season! You are trying to get all the exemptions and deductions that you can claim so that you are paying only the bare minimum tax requirement. At the end of the exercise, during filing the tax returns, you will know your effective tax rate . This rate can vary from 10% to 40%. Let's consider an average 30% Federal (including Social security and Medicare, don't forget these taxes!). In states like California, you are paying additional 10% State income tax . So your effective tax rate becomes 40% . It is definitely painful to shell out this much of your hard earned money. But it doesn't stop there. Add property tax on your house. Assuming $200K income and a $1MN home price, 1% property tax means $10,000 or 5% of the income. Your tax bill has already grown to 45% . If you are renting, your landlord will make sure to pass on the property tax they are paying, on to you. That's not enough either. Now let's assume that you are able to save 5% of...