Exam Question:

Two speakers emit sound waves of equal frequency and amplitude. Speaker A is located 5.0 meters to the left of speaker B. At a certain point, the waves from each speaker combine to produce a standing wave.

a) Explain what is meant by interference in the context of waves.

b) Determine the distance between consecutive nodes of the standing wave created by the interference of the waves from speaker A and speaker B.

c) Calculate the wavelength of the sound waves emitted by the speakers if the distance between consecutive nodes is 1.5 meters.

Answer:

a) Interference, in the context of waves, refers to the interaction of two or more waves traveling through the same medium at the same time. When waves meet, they superpose, or add up, resulting in constructive or destructive interference.

b) The distance between consecutive nodes of a standing wave is half the wavelength for the particular wave. In the given scenario, we have two waves interfering, and they are producing a standing wave. One complete wavelength corresponds to one complete constructive and one complete destructive interference, forming a node. Thus, the distance between consecutive nodes is half the wavelength of the sound wave.

c) Given that the distance between consecutive nodes is 1.5 meters, we can calculate the wavelength of the sound wave using the formula:

Wavelength = 2 * Distance between consecutive nodes

Substituting the given value:

Wavelength = 2 * 1.5 meters = 3.0 meters

Therefore, the wavelength of the sound waves emitted by speakers A and B is 3.0 meters.