Doppler Effect & Relative Motion — Practice · Grade 12 Science

Chapter: Waves, Sound & Optics

What this practice covers

By the end of Doppler Effect & Relative Motion you should be able to:

I can predict sound pitch changes with specified source/observer motion.
I can choose a sound formula and distinguish it from electromagnetic shift models.

8 questions, numeric and written answer, each with a worked explanation.

Vocabulary used: Doppler shift, redshift.

Problem 1

500 Hz source approaches at 10 m/s; v=350 m/s. Find fobs.

Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

514.71 Hz

500×350/340≈514.71.

Problem 2

Does source motion make sound travel faster through stationary air?

Answer and explanation

No; it changes front spacing, while medium properties largely determine speed.

Response criteria

State a scientifically accurate conclusion.
Show the calculation or mechanism that supports it.
Include units, conditions, or limits where relevant.

Problem 3

A 300 Hz source approaches at 20 m/s with sound speed 320 m/s. Find frequency for a stationary observer.

Hints

List the given quantities, select a relationship, and check units before substituting.

Answer and explanation

320 Hz

300×320/(320−20)=320.

Problem 4

Can the sound-source equation be used unchanged for starlight?

Answer and explanation

No. Light requires electromagnetic relativistic Doppler relationships.

Response criteria

State a scientifically accurate conclusion.
Show the calculation or mechanism that supports it.
Include units, conditions, or limits where relevant.

Problem 5

A 500 Hz source recedes at 34 m/s in the same model. Find received frequency. Show the reasoning, not just the conclusion.

Hints

The formula changes for moving observers or other geometries.

Answer and explanation

f'=500×340/(340+34)≈455 Hz.

Problem 6

Why should a sound Doppler formula not be copied unchanged for relativistic light?

Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Sound has a material medium and different source/observer roles; light requires the appropriate relativistic model.

Problem 7

Original sound/light comparison; cosmological expansion requires an additional model beyond simple local recession.

Interpret the supplied visual. For longitudinal recession at 0.60c, what fraction of emitted frequency is received?

Answer and explanation

√(0.40/1.60)=0.50; the observed frequency is half under the stated inertial model.

Light in vacuum does not use a stationary air-like medium. Its relativistic Doppler shift depends on the observer–source geometry and consistent inertial-frame definitions. For longitudinal recession, fobs=femit√[(1−β)/(1+β)] with β=v/c. This differs from simply replacing sound speed by c in the moving-source formula. The low-speed approximations can be similar, but their underlying assumptions and behavior at high speed differ.

√(0.40/1.60)=0.50; the observed frequency is half under the stated inertial model.

Response criteria

Interpret labels, structures, axes, units and directions correctly.
Explain the physical or environmental relationship or mechanism.
Respect stated assumptions and distinguish observation from inference.

Problem 8

A 600 Hz source recedes at 30 m/s from a stationary observer in still air with sound speed 330 m/s. Find received frequency and compare with the approach case at the same speed.

Answer and explanation

Receding:600×330/360=550 Hz. Approaching:600×330/300=660 Hz. The shifts are not symmetric about 600 in this finite-speed source model.

Receding:600×330/360=550 Hz.

Approaching:600×330/300=660 Hz.

The shifts are not symmetric about 600 in this finite-speed source model.

Response criteria

Use the stated measurements or conditions, with correct units.
Connect the result to the physical or environmental mechanism or evidence relationship.
Identify the assumption, model limit or further evidence requested.

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