Two loudspeakers 42.0 m apart and facing each other emit...

Two loudspeakers $42.0 \mathrm{m}$ apart and facing each other emit identical 115 Hz sinusoidal sound waves in a room where the sound speed is $345 \mathrm{m} / \mathrm{s} .$ Susan is walking along a line between the speakers. As she walks, she finds herself moving through loud and quiet spots. If Susan stands $19.5 \mathrm{m}$ from one speaker, is she standing at a quiet spot or a loud spot?

Key Concepts

Standing Waves

Standing waves arise from the interference of two waves traveling in opposite directions, resulting in a pattern of nodes (points of no displacement) and antinodes (points of maximum displacement). In setups with sound sources facing each other, the interference pattern can often be described as standing waves.

Path Difference

Path difference is the difference in the distances traveled by two waves from their respective sources to a common point. It is crucial in determining whether the waves will interfere constructively or destructively, as this difference directly relates to the phase difference between the waves.

Wave Interference

Wave interference is the phenomenon where two or more waves superimpose to form a resultant wave. When waves from coherent sources meet, they can add constructively (increasing amplitude) or destructively (decreasing or even canceling amplitude), leading to patterns of high and low intensity.

Constructive Interference

Constructive interference occurs when waves are in phase and their crests and troughs align, resulting in a higher amplitude at that point. This concept explains the formation of regions with increased sound intensity, often referred to as loud spots.

Destructive Interference

Destructive interference takes place when waves are out of phase, so that the crest of one wave aligns with the trough of another, effectively canceling each other out and creating regions of reduced or zero amplitude, known as quiet spots or nodes.

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