Question

Figure 12–32 shows various positions of a child on a swing moving toward a person on the ground who is blowing a whistle. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

Short answer

The highest frequency of sound will be heard at position C while the child is swinging forward.

Step-by-step solution

Understanding Simple Harmonic Motion

Simple Harmonic Motion is repetitive back and forth movement through an equilibrium so that the maximum displacement on one side of the equilibrium position is equal to the maximum displacement on the other side.

The force responsible for the motion is always directed toward the equilibrium position and is directly proportional to its distance.

Detailed Explanation

Let us assume that the child is moving with Simple Harmonic Motion (SHM), and in SHM, the highest speed is at the equilibrium point. Thus the highest speed of the child is at the equilibrium point, point C. And to have an increased pitch, the relative motion of the source and detector must be toward each other. The child would also hear the lowest frequency of sound at point C while swinging backward.

Hence, the highest sound frequency will be heard at position C when the child is swinging forward, while the lowest sound frequency will be heard at position C when the child is swinging backward.