Physics Help: How far when minimum sound is heard?

Question

Two speakers are driven by the same oscillator with frequency of 215 Hz. They are located 3.59 m apart on a vertical pole. A man really far away walks straight toward the lower speaker in a direction perpendicular to the pole. How far is he from the pole at the first moment he hears a minimum in sound intensity (short of infinity) if the speed on sound is 330 m/s?

Can anyone tell me how to get this one started?

Answer 1

Given the conditions of the two speakers (namely sharing the same frequency), they should also have the same wavelength, as v=fλ, since the speed of sound will also be the same (since they're going through the same medium).

When two waves interfere, they may interfere constructively or destructively. In any interference, the amplitudes of the wave at a specific time are added together. When both amplitudes are in the same direction, their amplitudes add together constructively to form a sound twice as loud. On the other hand, when both amplitudes are in opposite directions, the sum of their amplitudes at that time should be a minimum (zero if the magnitudes are the same and the sound is measured at a single point). This latter case is destructive interference, as it will make the sound significantly less loud, if it makes any noise at all.

Destructive interference occurs when the difference in the path taken by each wave is equal to λ/2. This makes sense, because at two points distance λ/2 along a sinusoidal wave (sine or cosine), they will be at equal but opposite amplitudes. Thus, you must find the the length of the path taken by each wave to a point x distance away from the lower speaker (where x will be the distance you're solving for), and find when the difference in paths is equal to λ/2.

Geometrically, the distance to the higher speaker will be √(x² + 3.59²), by the Pythagorean Theorem.

Answer 2

Apparently one speaker is head high on the pole and the other is 3.59 m higher? You need to set up the trigonometry to find the difference in distance (d1) to the one that is head high and distance (d2) to the higher one.

When the man is at a point such that the difference d1-d2 is 1/2 of a wavelength, the node and antinode will cancell out so the sound will be minumum.

Answer 3

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