Problem 1 - University Physics with Modern Physics

Question

Fans at a local football stadium are so excited that their team is winning that they start "the wave" in celebration. Which of the following four statements is (are) true? I. This wave is a traveling wave. II. This wave is a transverse wave. III. This wave is a longitudinal wave. IV. This wave is a combination of a longitudinal wave and a transverse wave. a) I and II c) III only e) I and III b) II only d) I and IV

Step-by-Step Solution

Answer

a) Transverse wave only b) Longitudinal wave only c) Both transverse and longitudinal waves d) Combination of transverse and longitudinal waves in a traveling wave Answer: d) Combination of transverse and longitudinal waves in a traveling wave

Step 1: Understand the characteristics of a traveling wave

A traveling wave is a type of wave that moves through a medium, transferring energy from one point to another. In this case, "the wave" is initiated by the fans and moves around the stadium in celebration. Since the wave is moving through the medium (i.e., the fans in the stadium), it is a traveling wave.

Step 2: Define transverse and longitudinal waves

Transverse waves are characterized by oscillations or vibrations occurring perpendicular to the direction of energy transfer, while longitudinal waves have oscillations parallel to the direction of energy transfer. In other words, in a transverse wave, the particles of the medium move up and down, and in a longitudinal wave, the particles of the medium compress and expand along the direction of the wave.

Step 3: Analyze the wave in the context of a football stadium

In "the wave" created by fans in a stadium, fans stand up and sit down as the wave passes, causing a noticeable motion that moves horizontally along the stadium rows. We observe up and down motion of fans (transverse motion), but we also see that fans transfer energy by influencing others to stand up and sit down in the same direction as the wave's movement (longitudinal motion). Thus, "the wave" in a football stadium context has both transverse and longitudinal characteristics.

Step 4: Select the correct answer

Based on our analysis, we concluded that "the wave" is a traveling wave (I), has characteristics of both transverse and longitudinal waves, making it a combination of both types (IV). Therefore, the correct answer is d) I and IV.