∙A father and his daughter are interested in the same...

$\bullet$ A father and his daughter are interested in the same baseball game. The father sits next to his radio at home and listens to the game; his daughter attends the game and sits in the outfield bleachers. In the bottom of the ninth inning a home run is hit. If the father's radio is 132 $\mathrm{km}$ from the radio station, and the daughter is 115 $\mathrm{m}$ from home plate, who hears the home run first? (Assume that there is no time delay between the baseball being hit and its sound being broadcast by the radio station. In addition, let the speed of sound in the stadium be 343 $\mathrm{m} / \mathrm{s.}$ .

$\bullet$ A father and his daughter are interested in the same baseball
game. The father sits next to his radio at home and listens to
the game; his daughter attends the game and sits in the outfield
bleachers. In the bottom of the ninth inning a home run is hit.
If the father's radio is 132 $\mathrm{km}$ from the radio station, and the
daughter is 115 $\mathrm{m}$ from home plate, who hears the home run first?
(Assume that there is no time delay between the baseball being hit
and its sound being broadcast by the radio station. In addition, let
the speed of sound in the stadium be 343 $\mathrm{m} / \mathrm{s.}$ .

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Key Concepts

Sound Wave Propagation

Sound waves travel at a finite speed through a medium—for example, in air at about 343 meters per second. This means that the time it takes for sound to travel from its source to an observer depends directly on the distance between them, resulting in a noticeable delay if the observer is far from the source.

Electromagnetic Wave Propagation

Electromagnetic waves, such as those used in radio broadcasts, travel at the speed of light, which is many orders of magnitude faster than the speed of sound. Due to this high speed, any transmission of audio signals via radio experiences an almost negligible delay compared to the delay experienced by sound waves traveling directly through the air.

Transmission Delay

Transmission delay refers to the time taken for a signal to travel from its source to a receiver. It is determined by the distance the signal must cover and the speed at which it propagates. In scenarios comparing sound and radio signals, even if the source-to-receiver distances are large, the delay for electromagnetic signals is minimal compared to that of sound, leading to differences in the receipt time of the same event.

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