IB Physics SL C.5 Doppler effect questions

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Question 1

Paper 2Easy9 marks

A sound source emits a steady tone into still air. Its emitted frequency is $f_s$ in both situations shown in Figure 1. The figure shows successive wavefronts along the line of motion at one instant. In A, the source is fixed and O moves as indicated. In B, the source moves as indicated while O₁ and O₂ are stationary. The diagrams are schematic; compare only the separations of adjacent wavefronts.

(a)

Describe the spacing of the wavefronts in A and state whether motion of O changes their spacing in the air.

[2]

(b)

Explain whether the frequency heard by O is higher or lower than $f_s$

[2]

(c)

In B, state the direction in which the source moves and compare the wavefront spacing ahead of and behind it.

[3]

(d)

State whether O₁ hears a frequency higher or lower than $f_s$

[1]

(e)

State whether O₂ hears a frequency higher or lower than $f_s$

[1]

Question 2

Multiple choiceMedium1 mark

A source emits light at a frequency of $5.000\times10^{14}\,\text{Hz}$ in its own rest frame. The source and observer move as shown in Fig. 1 at constant speeds, both much less than $c$ What frequency is measured by the observer?

Show answer and explanation

Answer: B. The source and observer move in the same direction, but the source is faster, so it approaches the observer at a relative speed of $0.00200c$ The wavefronts are encountered more frequently, giving a fractional frequency increase of $0.00200$ Thus $f_{\text{obs}}=(5.000\times10^{14})(1+0.00200)=5.010\times10^{14}\,\text{Hz}$

A: Uses the observer’s speed alone, predicting a $0.00100$ decrease in frequency.
C: Uses the source’s speed alone and ignores the observer’s motion.
D: Adds the speeds despite their being in the same direction, giving a fractional increase of $0.00400$

Remember: for motion in the same direction, the relative speed is the difference between the speeds.

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