# IBDP Physics C.5 Doppler effect IB Style Question Bank : HL Paper 2

### Question

A girl looks at a flat vertical glass window on an automobile. The window has a thin transparent coating.

White light from a source is reflected to the girl from the coating and from the window.

(a) Outline why the light reflected to the girl has one wavelength missing. [2]

(b) The refractive index of the coating is 1.63 and the refractive index of the glass is 1.52 .
The thickness of the coating is $$143 \mathrm{~nm}$$.
Determine the wavelength, in $$\mathrm{nm}$$, that is missing in the light reflected to the girl assuming that the light is incident normally on the window.[3]

(b) The refractive index of the coating is 1.63 and the refractive index of the glass is 1.52 . The thickness of the coating is $$143 \mathrm{~nm}$$.
Determine the wavelength, in $$\mathrm{nm}$$, that is missing in the light reflected to the girl assuming that the light is incident normally on the window. [3]

(c) The automobile is driven directly away from the girl at a steady speed of $$15 \mathrm{~m} \mathrm{~s}^{-1}$$. A musical note is emitted by a loudspeaker in the automobile.
The frequency of the musical note heard by the girl is $$410 \mathrm{~Hz}$$.
(i) Outline why the driver of the automobile and the girl hear different frequencies for the musical note.[2]
(ii) The speed of sound in air is $$330 \mathrm{~ms}^{-1}$$.
Calculate the frequency of the musical note emitted by the loudspeaker.[2]

Ans:

There is «partialm reflection at the front surface of the layer and also at the glasslayer interface $$\checkmark$$
destructive interference «between these reflections occurs at the missing wavelength

b Use of $$2 d n=m \lambda \checkmark$$
Use of $$n=1.63$$
470 «nm»

c i. There is relative motion between the girl and the automobile «Relative to the girl» the wavelength of the sound changes/increases $$\checkmark$$

c ii. Use of $$f=f^{\prime}\left(\frac{c+u}{c}\right)$$. $$\alpha f=410\left(\frac{330+15}{330}\right)=430 \alpha \mathrm{Hz}$$

### Question

Sound of frequency f = 2500 Hz is emitted from an aircraft that moves with speed v = 280 ms–1 away from a stationary observer.

The speed of sound in still air is c = 340 ms–1.

1. frequency heard by the observer. [2]

2. wavelength measured by the observer. [1]

f’ = 2500 × $$\frac{340}{340+280}$$
ii λ = $$\frac{340}{1371}$$ ≈ 0.24 / 0.25 «m »