(numerical problems)
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| Hmw 1 and Hmw 2 Solutions (numerical problems) |
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| 1) Problem: Radio Station Wavelength. Determine the wavelength from your group's favorite radio station and calculate how long it takes for the radio waves to arrive at your current location from the radio station. Solution: Let's say that my favorite radio station is at 2.5 km from my home. Let's also say that the frequency at which the radio station is emitting is 9.2 MegaHertz. Then the time the radio waves need to reach my home from the station can be calculated in the following way: the speed of all electromagnetic waves is the speed of light c = 3x108 m/s speed=distance / time this means that time = distance / speed=2.5 km/ 3x108 m/s = 2.5x103 m / 3x108 m/s=8.3x10-6s. This is almost one hundredthousandth of a second !!! Very small amount of time. The wavelength can be calculated using the fomula c=λ f where λis the wavelength and f is the frequency. So we have λ=c / f = 3x108 m/s / 9 .2Mega Hertz= 3x108 m/s / 9 .2 x106 1/s=32.60 m Radio waves are quite long waves, this one is almost big as 1/3 of a football field length. | ||||||
| 2) Problem: Doppler Shift. Calculate what the new wavelength for a 2 kHz automobile horn would be for a car moving first toward you and then away from you at a speed agreed upon by your group. Solution Let's say the car is moving at 10 m/s. The speed of sound is about 343.7 m/s. The first thing to do is to calculate the wavelength of the source at 2000 Hz (2KHz). You can follow method above and find out that the wavelength is 0.171 m. Then we can apply the following formula for the approching car λapproaching=(vsound-vsource)/fsource =(343.7 m/s -10 m/s) / 2000 Hz=0.151 m (shorter wavelength than stationary source wavelength) for the receding source we have λreceding=(vsound+vsource)/fsource =(343.7 m/s +10 m/s) / 2000 Hz=0.191 m (longer wavelength than stationary source wavelength). | ||||||