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Date	November 2019	Marks available	2	Reference code	19N.3.HL.TZ0.6
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Calculate	Question number	6	Adapted from	N/A

Question

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.

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

[2]

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

ALTERNATIVE 1
as the photons move away from the black hole, they lose energy in the gravitational field ✔
since $E = h f$ «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 $f = \frac{1}{T}$ , «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.

time between pulses = 3 s according to the probe ✔

$∆ t = « \frac{3}{\sqrt{1 - \frac{1}{1.5}}} = » 5.2$ «s» ✔

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Syllabus sections

Option A: Relativity » Option A: Relativity (Additional higher level option topics) » A.5 – General relativity (HL only)

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