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Chapter 37: 34P (page 1147)

A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of 位o=589nm. Wavelength 位is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift 位-位o?

Short Answer

Expert verified

The wavelength shift for sodium light source is 2.97 nm.

Step by step solution

01

Identification of given data

The proper wavelength of emitting light is 位o=589nm

The speed of sodium light source is u=0.1c

The wavelength shift is the variation in the wavelength of light due to relative movement of source and observer in different frames. It is calculated by the wavelength shift formula.

02

Determination of wavelength shift for sodium light source

The wavelength shift for sodium light source is given as:

位-位o=位o11-vc2-1

Substitute all the values in the above equation.

位-位o=589nm11-0.1cc2-1位-位o=2.97nm

Therefore, the wavelength shift for sodium light source is 2.97 nm.

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Most popular questions from this chapter

Sam leaves Venus in a spaceship headed to Mars and passes Sally, who is on Earth, with a relative speed of 0.5c . (a) Each measures the Venus鈥揗ars voyage time. Who measures a proper time: Sam, Sally, or neither? (b) On the way, Sam sends a pulse of light to Mars. Each measures the travel time of the pulse. Who measures a proper time: Sam, Sally, or neither?

The car-in-the-garage problem. Carman has just purchased the world鈥檚 longest stretch limo, which has a proper length of Lc=30.5鈥尘. In Fig. 37-32a, it is shown parked in front of a garage with a proper length of Lg=6.00鈥尘. The garage has a front door (shown open) and a back door (shown closed).The limo is obviously longer than the garage. Still, Garageman, who owns the garage and knows something about relativistic length contraction, makes a bet with Carman that the limo can fit in the garage with both doors closed. Carman, who dropped his physics course before reaching special relativity, says such a thing, even in principle, is impossible.

To analyze Garageman鈥檚 scheme, an xc axis is attached to the limo, with xc=0 at the rear bumper, and an xg axis is attached to the garage, with xg=0 at the (now open) front door. Then Carman is to drive the limo directly toward the front door at a velocity of 0.9980c(which is, of course, both technically and financially impossible). Carman is stationary in the xcreference frame; Garageman is stationary in the role="math" localid="1663064422721" Xgreference frame.

There are two events to consider. Event 1: When the rear bumper clears the front door, the front door is closed. Let the time of this event be zero to both Carman and Garageman: tg1=tc1=0. The event occurs at xg=xc=0. Figure 37-32b shows event 1 according to the xg reference frame. Event 2: When the front bumper reaches the back door, that door opens. Figure 37-32c shows event 2 according to the xg reference frame.

According to Garageman, (a) what is the length of the limo, and what are the spacetime coordinates (b) xg2 and (c) tg2 of event 2? (d) For how long is the limo temporarily 鈥渢rapped鈥� inside the garage with both doors shut? Now consider the situation from the xc reference frame, in which the garage comes racing past the limo at a velocity of 鈭�0.9980c. According to Carman, (e) what is the length of the passing garage, what are the spacetime coordinates (f) Xc2and (g) tc2 of event 2, (h) is the limo ever in the garage with both doors shut, and (i) which event occurs first? (j) Sketch events 1 and 2 as seen by Carman. (k) Are the events causally related; that is, does one of them cause the other? (l) Finally, who wins the bet?

Quite apart from effects due to Earth鈥檚 rotational and orbital motions, a laboratory reference frame is not strictly an inertial frame because a particle at rest there will not, in general, remain at rest; it will fall. Often, however, events happen so quickly that we can ignore the gravitational acceleration and treat the frame as inertial. Consider, for example, an electron of speed v =0.992c, projected horizontally into a laboratory test chamber and moving through a distance of 20 cm. (a) How long would that take, and (b) how far would the electron fall during this interval? (c) What can you conclude about the suitability of the laboratory as an inertial frame in this case?

Reference frame S鈥� is to pass reference frame S at speed v along the common direction of the and x axes, as in Fig. 37-9. An observer who rides along with frame S鈥� is to count off a certain time interval on his wristwatch. The corresponding time interval 鈭�t is to be measured by an observer in frame S. Figure 37-22 gives 鈭�tversus speed parameter 尾for a range of values for . The vertical axis scale is set by ta 14.0 s. What is interval 鈭�t if v = 0.98c?

What is the speed parameter for the following speeds: (a) a typical rate of continental drift (1 in./y); (b) a typical drift speed for electrons in a current-carrying conductor (0.5 mm/s); (c) a highway speed limit of 55 mi/h; (d) the root-mean-square speed of a hydrogen molecule at room temperature; (e) a supersonic plane flying at Mach 2.5 (1200 km/h); (f) the escape speed of a projectile from the Earth鈥檚 surface; (g) the speed of Earth in its orbit around the Sun; (h) a typical recession of a distant quasar due to the cosmological expansion 3脳104kms-1.
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