Find Min Radius for Sound Wave in Tube

In summary, the problem involves finding the minimum radius of the circular tube shown in the figure, in order for constructive interference to occur at the detector end and produce a minimum. The solution involves considering the difference in lengths traveled by the sound wave along the straight and circular tubes, and using the equation v = λf to relate wavelength, frequency, and speed of sound.
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Homework Statement


"A sound wave of 40.0 cm wavelength enters the tube shown below at the source end. What must be the smallest radius r such that a minimum will be heard at the detector end?" (figure attached)

Homework Equations


v =[tex]\lambda[/tex][tex]f[/tex]

The Attempt at a Solution


I don't have any idea how to do this problem. My first idea was to use the formula for the wavelength of a closed or open tube, but whether the tube is closed or open isn't given so I'm guessing that's not right. Also, I don't see how the radius of the half circle has anything to do with the tube through which the sound is traveling.

Thanks in advance
 

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  • #2
The sound travels along both the straight tube and the circular one. The sound wave enters in both tubes with the same phase, but the lengths the waves travel along the different segments will be different. What is the minimum difference between the lengths traveled so as destructive interference occur at the other end of the circular tube?

ehild
 

What is the "Find Min Radius for Sound Wave in Tube" experiment?

The "Find Min Radius for Sound Wave in Tube" experiment is a scientific investigation to determine the minimum radius of a tube that will allow a sound wave to propagate through it without distortion. This experiment is important in understanding acoustic properties and can have practical applications in engineering and design.

Why is it important to know the minimum radius for a sound wave in a tube?

Knowing the minimum radius for a sound wave in a tube is important because it allows for the design and construction of efficient and effective acoustic devices. It also helps in predicting and avoiding acoustic resonance, which can cause damage to structures and equipment.

How is the minimum radius for a sound wave in a tube determined?

The minimum radius for a sound wave in a tube is determined through a series of experiments where the tube's radius is gradually decreased and the sound wave's amplitude and frequency are measured. The point at which the sound wave can no longer propagate without distortion is considered the minimum radius.

What factors can affect the minimum radius for a sound wave in a tube?

Several factors can affect the minimum radius for a sound wave in a tube, including the material of the tube, the temperature and pressure of the surrounding environment, and the characteristics of the sound wave itself (such as frequency and amplitude). The shape and design of the tube can also play a role in determining the minimum radius.

How can the results of the "Find Min Radius for Sound Wave in Tube" experiment be applied in real-world scenarios?

The results of this experiment can be applied in various real-world scenarios, such as designing musical instruments, creating efficient acoustic insulation, and optimizing the performance of exhaust systems in vehicles. It can also be used in the design and construction of buildings and structures to prevent acoustic resonance and improve sound quality.

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