Hello, can someone please check my answers and tell me if they are correct?
1. A laser produces a pulse of light with a speed of 300000000m/s in vacuum in a time 1.70x10^-15s.
a) what is the length of the pulse?
b) The pulse travels into a piece of glass in which it's lenghth is 3.75x10^-7m. What is the speed of light in the glass.
My answers were 5.10x10^-7m and 2.21x10^8 m/s respectively.
2. You flick a rope, sending a pulse down it toward your friend. If the pulse takes 1.81s to travel the length of the 10 m rope, and has a length of 1.16m, how long did it take you to produce it?
My answer was 2.10x10^-1s.
3. Most radio stations use antennas which are a quarter of the length of the wavelength they produce.
a)One FM radio station has a frequency of 88.5 MHz. Radio, like all forms of electromagnetic radiation, travels at a speed of about 3.00x10^8 m/s in air. How long should the antenna for this FM radio station be?
b) A typical AM radio station has a frequency of 530 kHz. How long should the antenna be for this radio station?
My answers were 8.47x10^-1m and 1.42x10^2m respectively.
4. The musical note G6 has a frequency of 1568 Hz. If the speed of sound in an auditorium is 347m/s, what is the wavelength of G6 in the auditorium.
My answer was 0.221m.
Thanks!
3a. L = V/F = 3*10*8/8.85*10^7 = 3.39 m = Wavelength.
La = 1/4 * 3.39 = 0.85 m. = Length of antenna.
b. L = V/F = 3*10^8/5.3*10^5 = Wavelength.
1/4 * wavelength = Length of antenna.
4. L = V/F = 347/1566 = 0.222 M.
1. Let's start with the first question. To find the length of the pulse, we can use the formula:
Length = Speed x Time
a) Using the given speed of light in vacuum (300000000 m/s) and the time (1.70x10^-15 s), we can calculate the length of the pulse:
Length = 300000000 m/s x 1.70x10^-15 s
= 5.1x10^-7 m
So your answer for the length of the pulse is correct (5.1x10^-7 m).
b) To find the speed of light in the glass, we can use the formula:
Speed = Distance / Time
Given the length of the pulse in the glass (3.75x10^-7 m) and the time (1.70x10^-15 s), we can rearrange the formula:
Speed = 3.75x10^-7 m / 1.70x10^-15 s
≈ 2.21x10^8 m/s
So your answer for the speed of light in the glass is correct (2.21x10^8 m/s).
2. In this question, we are asked to find the time it took to produce a pulse that traveled down a 10 m rope. Given the length of the pulse (1.16 m) and the time it took to travel (1.81 s), we can use the formula:
Speed = Distance / Time
Since distance is given and speed is constant, we can calculate the time it took to produce the pulse:
Time = Distance / Speed
= 1.16 m / 10 m/s
= 0.116 s
So your answer for the time it took to produce the pulse is incorrect. It should be 0.116 s, not 2.10x10^-1 s.
3. Let's move on to the next question about radio station antennas.
a) To find the length of the FM radio station antenna, we first need to calculate the wavelength using the formula:
Wavelength = Speed / Frequency
Given the frequency of 88.5 MHz (88.5x10^6 Hz) and the speed of light in air (3.00x10^8 m/s), we can calculate the wavelength:
Wavelength = 3.00x10^8 m/s / 88.5x10^6 Hz
≈ 3.39 m
Since the antenna length is a quarter of the wavelength, we can calculate it:
Antenna Length = 1/4 x Wavelength
= 1/4 x 3.39 m
= 8.47x10^-1 m
So your answer for the antenna length of the FM radio station is correct (8.47x10^-1 m).
b) Similarly, for the AM radio station with a frequency of 530 kHz (530x10^3 Hz), we can calculate the wavelength:
Wavelength = 3.00x10^8 m/s / 530x10^3 Hz
≈ 5.66x10^2 m
The antenna length would be a quarter of the wavelength:
Antenna Length = 1/4 x Wavelength
= 1/4 x 5.66x10^2 m
= 1.42x10^2 m
So your answer for the antenna length of the AM radio station is correct (1.42x10^2 m).
4. Finally, to find the wavelength of the musical note G6 with a frequency of 1568 Hz and the speed of sound in the auditorium (347 m/s), we can use the formula:
Wavelength = Speed / Frequency
Wavelength = 347 m/s / 1568 Hz
≈ 0.221 m
So your answer for the wavelength of G6 in the auditorium is correct (0.221 m).
Overall, your answers for questions 1a, 1b, 3a, 3b, and 4 are correct. However, your answer for question 2 is incorrect. It should be 0.116 s instead of 2.10x10^-1 s.