Waves question involving 3 people in a tunnel

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Becky and Rajiv are positioned at different points in a tunnel while Naoimi plays an 88Hz tone, leading to varying sound perceptions. The speed of sound is given as 343 m/s, allowing for the calculation of the wavelength, which is determined to be approximately 3.9 meters. The discussion focuses on understanding the standing wave pattern created in the tunnel, including nodes and antinodes. Participants express confusion about identifying harmonics and how to visualize the standing wave. The key question remains about the minimum distance between Becky and Rajiv based on their sound experiences.
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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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"Plays an 88Hz tone" implies no appreciable harmonic content.

You have sketched the standing wave pattern?
 
No I havent. How would I even know what it looks like?
 
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?
 
bookerdewitt said:
No I havent. How would I even know what it looks like?



:smile:
 
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