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ShockWave AdventurePHYS 101 LG2 Learning Object #1

After exams finished, you and your family decide to go to Six Flags Over

Texas, for the ShockWave ride that has recently been renovated. Known for

giving all its riders the harmonic wave experience, riders are tied down to a

flexible structure that models a harmonic wave, which is generated by a

large spring undergoing simple harmonic motion. Being acrophobic, you

decide to bring walkie-talkies so you feel safer.

A) Upon arriving in Texas, you realize that there are very specific instructions on

the range of the walkie-talkies. You and your father must be a horizontal

distance of exactly 10m away at all times. As part of the theme of ShockWave,

seats are chosen by phase. Looking at the following attraction guide showing the

time plot for a specific seat, what is the wavelength of the ride?

Wave speed = 4m/s

1 2 3

4

Wave speed = 4m/s

1 2 3 4

To find the wavelength we use the relationship

We know that from

the time plot, we can

find the period,

which is the time

taken for one

complete wave

cycle.

Wave speed is also

given as 4m/s

Period (T) = 2s

B)When choosing your seats, what must be the phase difference

between you and your dad’s seat so that the horizontal distance (∆x)

between you and your dad will be exactly 10m during the ride?

10 m

Note: graph is not drawn to scale

To do this problem, we must understand that the horizontal distance between two points in a

harmonic wave remains the same as the medium does not travel with the wave

We must also understand the concept of phase:

Phase: The argument of Sine/Cosine, essentially what the trig functions are being applied to

at a specific position and time

Ex:

Phase

We consider their phase at a given time t:

Note they have the same and as they are both on the same harmonic wave, just at

different positions

Where k is the wave number (a measure of change of phase)

We know that ∆x = 10m and we use the relationship between wave number and

wavelength

C)By accident, you dropped your walkie-talkie during the first ride but would like to go on again. To feel safe, you want to make sure that at every peak, your father will be able to see you directly ahead. Which description below is correct about your seating arrangement?

DadYou

1)You and your father are out of phase

2)You and your father are π/2 out of phase

3)You and your father are in phase

4)You are your father are 10m apart

DadYou

In Phase: 2 points described as in phase in a harmonic wave are a phase difference of 2π (or even multiples of π) away. Points in phase have equal displacement (D) from the equilibrium position at all times. In this case they would be 2π away specifically, or the Dad’s vision would be obstructed (if 4π apart, there would be another person in between)

Since the Dad needs to be able to have vision on you directly at the peak, he must have the same displacement from the equilibrium position as you, which is a characteristic of two points in phase.

Another way to prove that it is in phase is to notice that you and your Dad are exactly one wavelength away.

Knowing that and that ∆x = λ, the phase difference is 2π, satisfying the condition of two points in phase

D) You discover that there are many other variations of shockwave. Assuming that the phase difference between you and your dad remains the same (you choose the same seats), which variations can you go on while making sure that your dad will still have clear vision of you directly ahead at the peak?

a) Variation of Shockwave with higher amplitude

b) Variation of Shockwave with smaller wavelength

c) Variation of Shockwave with a higher wave speed

d) both B and C are correct

e) A, B and C

II

D) This is because the Phase Difference between you and your dad are always 2π, since the same seats are always chosen at every variation

This means that you and your Dad will always be in phase!

Knowing that , If the phase difference is always 2π, ∆x will always equal λ. This means that if wavelength is increased, the distance between you and your dad will also increase to be exactly one wavelength apart.

Similarly, wave speed can also change the wavelength, which follows the same concept as above, as the horizontal distance will change to equal the wavelength, given that the phase difference remains the same.

Finally, given that we know that a change in amplitude only affects the displacement from the equilibrium point and not the phase. Therefore, if your Dad and you still have a phase difference of 2π, you will continue to both be at the same displacement at a given time (even though an increased displacement) and therefore still be in phase.

Picture Sources

By order of appearance

https://www.sixflags.com/overtexas/attractions/shock-wave

http://www.techyzone.com/technology/the-future-of-roller-coasters/

http://bsa-troop621.org/photographufm/displacement-time-graph

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html





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