How to work out the reflection point of waves

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Homework Help Overview

The problem involves determining the distance to a reflection point of waves generated by a workman striking a steel pipeline, specifically focusing on the time difference between the reflected longitudinal and transverse waves.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between wave speed, distance, and time, with some attempting to derive a formula based on the time difference between the two types of waves. Questions arise regarding the correct application of the equations and the interpretation of the given data.

Discussion Status

Some participants are exploring different approaches to derive the necessary formula, while others express confusion about the problem setup and the information provided. There is an ongoing exchange of ideas, with attempts to clarify the relationships between variables involved.

Contextual Notes

Participants note the lack of explicit values for time in the problem statement, which complicates their ability to apply the equations effectively. The discussion reflects a mix of understanding and uncertainty regarding the mathematical relationships involved.

CalinDeZwart
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Homework Statement



When a workman strikes a steel pipeline with a hammer, he generates both longitudinal and transverse waves. The two types of reflected waves return 2.4 s apart. How far away is the reflection point? (For steel, vL = 6.2 km/s, vT = 3.2 km/s).

Homework Equations



Unknown, this is where I need some guidance.

I have referred to the following:
Cutnell, J. D., & Johnson, K. W. (2015). Physics. (10th ed.). New York: John Wiley.
Serway, R.A., Jewett, J.W., Wilson, K., and Wilson, A. (2013). Physics. (Volume 2) (1st ed. Asia‐Pacific
Edition). South Melbourne, Australia: Cengage Learning Australia Pty. Ltd.

3. The Attempt at a Solution

I know the answer is 7.9 km.

Working backwards, I understand it would take V(L) 2.54 seconds and V(T) 4.94 seconds to complete their respective cycles, resulting in the 2.4 second gap.

What I am hoping for is someone who can get me on the right track with a formula to work with.

Thanks
 
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You should be able to arrive at the formula yourself through reasoning. Calling the distance to the reflection time x, how long does it take each wave to go back and forth? What is the difference between those times?
 
Thanks for your reply,

Unfortunately I cannot get my head around how to tackle this question. I know it is basic math, but it just won't click.
 
The best I could come up with t = (d*2) / v
d = (t/2) * v
However, the question doesn't provide data for t and d is the answer I need to arrive at (7.9)

What am I missing?
 
CalinDeZwart said:
The best I could come up with t = (d*2) / v
d = (t/2) * v
However, the question doesn't provide data for t and d is the answer I need to arrive at (7.9)

What am I missing?
Reread my first post and follow the steps it describes. Your equation for the time is correct, but the time is different for each wave - with each traveling at its own speed.
 
I worked it out I think.

2.4 = (2x/Vt) - (2x/Vl)
2.4 = (2x/3.2) - (2x/6.2)
1.2 = (x/3.2) - (x/6.2)

(1.2)(3.2)(6.2) = (6.2x) - (3.2x)

23.808 = 3.0x
x = 23.808/3.0
x = 7.936km
x = [7.9km]

Thanks for your help.