DATA Supernova! (a) Equation (16.30) can be written as f R = f S ( 1 − υ c ) 1 / 2 ( 1 + υ c ) − 1 / 2 where c is the speed of light in vacuum, 3.00 × 10 8 m/s. Most objects move much slower than this ( υ / c is very small), so calculations made with Eq. (16.30) must be done carefully to avoid rounding errors. Use the binomial theorem to show that if υ ≪ c , Eq. (16.30) approximately reduces to f R = f S [1 − ( υ / c )] . (b) The gas cloud known as the Crab Nebula can be seen with even a small telescope. It is the remnant of a supernova, a cataclysmic explosion of a star. (The explosion was seen on the earth on July 4, 1054 C.E.) Its streamers glow with the characteristic red color of heated hydrogen gas. In a laboratory on the earth, heated hydrogen produces red light with frequency 4.568 × 10 14 Hz; the red light received from streamers in the Crab Nebula that are pointed toward the earth has frequency 4.586 × 10 14 Hz. Estimate the speed with which the outer edges of the Crab Nebula are expanding. Assume that the speed of the center of the nebula relative to the earth is negligible. (c) Assuming that the expansion speed of the Crab Nebula has been constant since the supernova that produced it, estimate the diameter of the Crab Nebula. Give your answer in meters and in light-years. (d) The angular diameter of the Crab Nebula as seen from the earth is about 5 arc-minutes ( 1 arc-minute = 1 60 degree ). Estimate the distance (in light-years) to the Crab Nebula, and estimate the year in which the supernova actually took place.
DATA Supernova! (a) Equation (16.30) can be written as f R = f S ( 1 − υ c ) 1 / 2 ( 1 + υ c ) − 1 / 2 where c is the speed of light in vacuum, 3.00 × 10 8 m/s. Most objects move much slower than this ( υ / c is very small), so calculations made with Eq. (16.30) must be done carefully to avoid rounding errors. Use the binomial theorem to show that if υ ≪ c , Eq. (16.30) approximately reduces to f R = f S [1 − ( υ / c )] . (b) The gas cloud known as the Crab Nebula can be seen with even a small telescope. It is the remnant of a supernova, a cataclysmic explosion of a star. (The explosion was seen on the earth on July 4, 1054 C.E.) Its streamers glow with the characteristic red color of heated hydrogen gas. In a laboratory on the earth, heated hydrogen produces red light with frequency 4.568 × 10 14 Hz; the red light received from streamers in the Crab Nebula that are pointed toward the earth has frequency 4.586 × 10 14 Hz. Estimate the speed with which the outer edges of the Crab Nebula are expanding. Assume that the speed of the center of the nebula relative to the earth is negligible. (c) Assuming that the expansion speed of the Crab Nebula has been constant since the supernova that produced it, estimate the diameter of the Crab Nebula. Give your answer in meters and in light-years. (d) The angular diameter of the Crab Nebula as seen from the earth is about 5 arc-minutes ( 1 arc-minute = 1 60 degree ). Estimate the distance (in light-years) to the Crab Nebula, and estimate the year in which the supernova actually took place.
DATA Supernova! (a) Equation (16.30) can be written as
f
R
=
f
S
(
1
−
υ
c
)
1
/
2
(
1
+
υ
c
)
−
1
/
2
where c is the speed of light in vacuum, 3.00 × 108 m/s. Most objects move much slower than this (υ/c is very small), so calculations made with Eq. (16.30) must be done carefully to avoid rounding errors. Use the binomial theorem to show that if υ ≪ c, Eq. (16.30) approximately reduces to fR= fS [1 − (υ/c)]. (b) The gas cloud known as the Crab Nebula can be seen with even a small telescope. It is the remnant of a supernova, a cataclysmic explosion of a star. (The explosion was seen on the earth on July 4, 1054 C.E.) Its streamers glow with the characteristic red color of heated hydrogen gas. In a laboratory on the earth, heated hydrogen produces red light with frequency 4.568 × 1014 Hz; the red light received from streamers in the Crab Nebula that are pointed toward the earth has frequency 4.586 × 1014 Hz. Estimate the speed with which the outer edges of the Crab Nebula are expanding. Assume that the speed of the center of the nebula relative to the earth is negligible. (c) Assuming that the expansion speed of the Crab Nebula has been constant since the supernova that produced it, estimate the diameter of the Crab Nebula. Give your answer in meters and in light-years. (d) The angular diameter of the Crab Nebula as seen from the earth is about 5 arc-minutes ( 1 arc-minute =
1
60
degree ). Estimate the distance (in light-years) to the Crab Nebula, and estimate the year in which the supernova actually took place.
How fast would you need to be driving towards a red light for it to appear green to you due to the doppler shift?
Recall red light has a frequency of 4.6x1014 Hz and green light has a frequency of 5.5x1014 Hz.
Speed: ______ m/s
Convert the speed to mph using the conversion factor 1 m/s = 2.34 mph
Speed: _______ mph
A tuning fork has a frequency of 800 Hz and hence a period of 1.25 × 10 −3 s. If the tuning fork is in an inertial frame of reference moving by the observer at speed of 0.690 c, what is the frequency of the fork as measured by the observer? (Assume that measurements are strictly by optical means and that the speed of sound waves in air is not pertinent here).
a.
445 Hz
b.
579 Hz
c.
1 110 Hz
d.
1 440 Hz
e.
419 Hz
At 20°C, a student sets off a firecracker and hears the echo from the Physics building 1.3 seconds later. How far away is the Physics building in meters?
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