Waves question involving 3 people in a tunnel

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In summary, Becky and Rajiv are at different points in a long tunnel while Naomi adjusts her bass amplifier. Naomi plays an 88Hz tone and Raj complains that the volume is too loud. To find the minimum distance between Becky and Rajiv, the wavelength is calculated to be 3.9m. The standing wave pattern in the tunnel can be determined by treating it as a pipe of unknown length. The distance between nodes and antinodes in the standing wave will help determine the minimum distance between Becky and Rajiv.
  • #1
bookerdewitt
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Homework Statement


Becky and Rajiv are standing at different points in a long tunnel while Naoimi adjusts her bass amplifier at one end. As Naoimi plays an 88Hz tone, BEcky cannot hear much and Raj complains that the volume is too loud. What is the minimum distance between Becky and Rajiv?(Use 343 m/s for speed of sound).



Homework Equations


v=f x lambda
L=lambda/2 x n, n being the harmonic and L being the length




The Attempt at a Solution



So I calculated the wavelength as being 3.9m for the 88hz tone and I figure Raj must be closer to Naomi then Becky but I don't understand how you would know which harmonic the tone would be so I can't use the length formula at all.
 
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  • #2
"Plays an 88Hz tone" implies no appreciable harmonic content.

You have sketched the standing wave pattern?
 
  • #3
No I havent. How would I even know what it looks like?
 
  • #4
Treat the tunnel as a pipe of unknown length. The standing wave produced will have nodes and antinodes, alternating. How far apart will they be? Is it a node or antinode:
- at the loudspeaker
- at Becky
- at Rajiv?
 
  • #5
bookerdewitt said:
No I havent. How would I even know what it looks like?



:smile:
 
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FAQ: Waves question involving 3 people in a tunnel

1. What is the concept of waves in a tunnel involving 3 people?

Waves in a tunnel involving 3 people refer to the phenomenon of sound waves bouncing off the walls of a tunnel and creating echoes when there are 3 people present. This can also be seen in other types of waves such as light waves.

2. How do waves behave in a tunnel with 3 people?

Waves in a tunnel with 3 people behave similarly to waves in any other enclosed space. The sound waves will travel through the tunnel and bounce off the walls, creating echoes. The presence of 3 people in the tunnel may affect the amplitude and frequency of the waves due to their movement and positioning.

3. Why is it important to study waves in a tunnel with 3 people?

Studying waves in a tunnel with 3 people can provide insights into the behavior of waves in enclosed spaces and how they interact with different objects and obstacles. This knowledge can be applied in various fields such as acoustics, architecture, and engineering.

4. Can the distance between the 3 people in the tunnel affect the waves?

Yes, the distance between the 3 people in the tunnel can affect the waves. The closer the people are to each other, the more interference and distortion there may be in the waves. On the other hand, if the people are spread out, the waves may have a clearer path to travel without much interference.

5. How can the study of waves in a tunnel with 3 people be applied in real life scenarios?

The study of waves in a tunnel with 3 people can have practical applications in the design of concert halls, auditoriums, and other enclosed spaces where sound quality and acoustics are important. It can also be useful in understanding how sound travels in crowded spaces and how to minimize noise pollution in urban areas.

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