The diagram shows the various positions of a child in motion on a swing. Somewhere in front of the child a stationary whistle is blowing.
-At which position(s) will the child hear the same frequency as that heard by a stationary observer standing next to the whistle?
A)at both A and D
B)at B when moving toward A
C)at B when moving toward C
D)at C when moving toward B
E)at C when moving toward D

Question

The diagram shows the various positions of a child in motion on a swing. Somewhere in front of the child a stationary whistle is blowing. 
-At which position(s) will the child hear the same frequency as that heard by a stationary observer standing next to the whistle?
A)at both A and D 
B)at B when moving toward A 
C)at B when moving toward C 
D)at C when moving toward B 
E)at C when moving toward D

Quizplus · Accepted Answer

The frequency heard by an observer is given by the formula:

f = v/λ

where f is the frequency, v is the speed of sound, and λ is the wavelength.

When the child is at the highest point (position A), the distance between the whistle and the child is maximum, and therefore the wavelength is maximum. As the child swings down to position D, the distance between the whistle and the child decreases, and so does the wavelength. However, since the child is moving towards the whistle, the speed of sound relative to the child increases, which compensates for the decrease in wavelength, and the frequency heard remains the same.

Similarly, when the child is at position D, the distance and wavelength are minimum, but the child is moving away from the whistle, which again increases the speed of sound relative to the child and compensates for the decrease in wavelength, resulting in the same frequency being heard as by a stationary observer next to the whistle. Therefore, the answer is A) at both A and D.

The Diagram Shows the Various Positions of a Child in Motion