Two in-phase loudspeakers separated by distance d emit 170...

Two in-phase loudspeakers separated by distance $d$ emit $170 \mathrm{Hz}$ sound waves along the $x$ -axis. As you walk along the axis, away from the speakers, you don't hear anything even though both speakers are on. What are three possible values for d? Assume a sound speed of $340 \mathrm{m} / \mathrm{s}$.

Key Concepts

Wave Interference

Wave interference refers to the phenomenon that occurs when two or more waves superpose to produce a resultant wave of greater, lower, or the same amplitude. This concept is fundamental for understanding how overlapping sound waves can reinforce or cancel each other depending on their phase relationship.

Constructive and Destructive Interference

Constructive interference happens when the crest of one wave aligns with the crest of another, leading to an increase in amplitude, while destructive interference occurs when a crest meets a trough, resulting in a decrease or cancellation of the amplitude. The precise conditions for interference depend on the phase difference, which in turn is affected by the path difference between sources.

Wavelength and Frequency Relationship

The relationship between wavelength, frequency, and the speed of sound is described by the formula ? = v/f, where ? is the wavelength, v is the speed of sound in the medium, and f is the frequency. Understanding this relationship is crucial for predicting how waves propagate and interact, including the calculation of interference patterns.

Path Difference

The path difference between waves from separate sources is the difference in the distance each wave travels to reach a given point. This difference determines the phase difference at that point, which is key to whether the interference is constructive or destructive. In scenarios where waves cancel each other out, the path difference corresponds to an odd multiple of half wavelengths.

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