Video Transcript
Two waves, wave A and wave B, start
to travel from points that intersect a line perpendicular to their direction of
motion, as shown in the diagram. The waves travel through regions
containing media with different properties. Both regions are the same size. Wave A has a wavelength of 1.5
meters and a frequency of 50 hertz. Wave B has a wavelength of 2.5
meters and a frequency of 20 hertz. Which of the following statements
is correct? (A) Wave A reaches the end of the
region opposite to the end it started from before wave B does. (B) Wave A reaches the end of the
region opposite to the end that it started from after wave B does. Or (C) wave A and wave B reach the
end of the region opposite to the end that they started from at the same time.
To answer this question, we’ll need
to determine the speeds of the two waves. Since the waves start at the same
point and need to cover the same distance to get to the end, we know that the wave
with the greater speed reaches the end first. Now, we were told the wavelength
and frequency of each wave. So we should recall that we can
relate these quantities to a wave speed 𝑠 using the wave speed formula: 𝑠 equals
𝑓 times 𝜆, where 𝑓 is the frequency and 𝜆 is wavelength.
Let’s apply this formula to both
waves, starting with wave A. We were told that wave A has a
frequency of 50 hertz and a wavelength of 1.5 meters. Thus, we know that the speed of
wave A equals 50 hertz multiplied by 1.5 meters, giving us a result of 75 meters per
second.
Next, let’s find the speed of wave
B. We were told that wave B has a
frequency of 20 hertz and a wavelength of 2.5 meters. Therefore, it has a speed of 20
hertz multiplied by 2.5 meters, which gives us 50 meters per second.
We can tell then that wave A is
faster than wave B. This means wave A reaches the end
first. This corresponds to answer choice
(A), which is our final answer. Using the wave speed formula, we
know that wave A reaches the end of the region opposite to the end it started from
before wave B does.
