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Question 19N.3.HL.TZ0.6

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Date November 2019 Marks available [Maximum mark: 4] Reference code 19N.3.HL.TZ0.6
Level HL Paper 3 Time zone TZ0
Command term Calculate, Explain Question number 6 Adapted from N/A
6.
[Maximum mark: 4]
19N.3.HL.TZ0.6

A black hole has a Schwarzschild radius R. A probe at a distance of 0.5R from the event horizon of the black hole emits radio waves of frequency f that are received by an observer very far from the black hole.

(a)

Explain why the frequency of the radio waves detected by the observer is lower than f.

[2]

Markscheme

ALTERNATIVE 1
as the photons move away from the black hole, they lose energy in the gravitational field ✔
since E=hf «the detected frequency is lower than the emitted frequency» ✔

 

ALTERNATIVE 2
if the observer was accelerating away from the probe, radio waves would undergo Doppler shift towards lower frequency ✔
by the equivalence principle, the gravitational field has the same effect as acceleration ✔

 

ALTERNATIVE 3
due to gravitational time dilation, time between arrivals of wavefronts is greater for the observer ✔
since f=1T, «the detected frequency is lower than the emitted frequency» ✔

 

NOTE: The question states that received frequency is lower so take care not to award a mark for simply re-stating this, a valid explanation must be given.

(b)

The probe emits 20 short pulses of these radio waves every minute, according to a clock in the probe. Calculate the time between pulses as measured by the observer.

[2]

Markscheme

time between pulses = 3 s according to the probe ✔

∆t=«31-11.5=» 5.2 «s» ✔

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