Which of the following graphs best illustrates how the intensity of sound varies as a detector is moved further and further from a stationary source projecting sound in all directions? (Note: Ignore the Doppler effect)

Question

Quizplus · Accepted Answer

11ecba2d_1308_7adc_a3bf_834006a95de6_MD0008_00 Sound waves propagate energy by increasing and decreasing the pressure within consecutive segments of a medium through which they travel. The pressure gradient caused by sound wave propagation is related to the intensity (I) of the sound wave, which is defined as power (P) per unit area (A): 11ecba2d_1308_7add_a3bf_ad5417d4e6c7_MD0008_00 Although the power of sound waves is largely conserved when passing through a uniform medium (eg, air), the intensity of sound waves (and perceived loudness) is not. This phenomenon can be explained by the increased area onto which sound waves impart energy as the distance between source and detector increases. In the case of a single source of sound propagating sound waves in all directions, increasing area is best illustrated by a series of spheres with increasing radius (r) and surface area (A) as given by: 11ecba2d_1308_a1ee_a3bf_ddd8468295ac_MD0008_00 Substituting this equation into the equation relating intensity, power, and area yields: 11ecba2d_1308_a1ef_a3bf_c529fc2476aa_MD0008_00 Simplifying the above equation as a proportionality to isolate the relationship between intensity and radius (distance) results in: 11ecba2d_1308_a1f0_a3bf_4b2716f43a53_MD0008_00 Therefore, the intensity of sound projected in all directions is inversely proportional to the square of the distance between the source and the detector. (Choices A and B) For intensity to increase as distance between sound source and observer increases, the area onto which sound imparts energy would have to decrease. The reflection and scattering of sound makes such a scenario unlikely in everyday circumstances. (Choice C) Although the relationship between distance and sound intensity is inverse, the relationship is exponential, not linear. Educational objective: The intensity of sound waves is defined as power per unit area, and relates to the perceived loudness of sounds. Intensity is inversely proportional to the square of the distance between source and detector, resulting in a relatively significant decrease in intensity as the distance increases.

Which of the Following Graphs Best Illustrates How the Intensity