Two small identical speakers are connected (in phase) to the same source. The sp

Question

Two small identical speakers are connected (in phase) to the same source. The speakers are 3m apart and at ear level. An observer stands at x, 4 m in front of one of the speakers as shown in the diagram and experiences a minimum in intensity. What is the shortest distance in a downward direction tht the observer should move to experience a maximum in intensity?

A.5m

B.4m

C.3m

D. 2m

E.1m

I believe answer should be 3m. I do not know how to arrive at that answer. I would greatly appreciate it if the answer would be given in terms of the equations provided below. Thank you in advance.

Explanation / Answer

This looks like a question about interference. Sound reaches the observer's ear (we shall assume he or she has just one, for the sake of simplicity) by two paths, namely from each of the two speakers. We should assume that no other paths (for example from reflecting surfaces) complicate the situation.

If sounds arriving over the two paths arrive in phase, then the sound will be loudest. If they arrive in antiphase then the sound will be weakest. The phase difference depends on the path difference (d) for the two sounds. For constructive interference d will be an integral number (n) of wavelengths.

In this question, we can draw a right-angle triangle ABC where A and B are the two speakers, 3m apart, C is a point 4m from A, AC being at right angles to AB. CB is the hypotenuse.

The path difference is=shortest distance = CB - AC = sqrt(3^2 + 4^2) - 4 = 1m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.