Interference of Sound Waves in a Circular Tube

[JeanDucreaux]

1. A sound wave with frequency f = 2300Hz is sent into a circular tube of radius R=160cm through an opening at some point A.
A receiver lies at point B, separated from A by an angle α=130°. The speed of sound in air is v=330 m/s.
Sound propagates from A to B in both directions along the tube.
(a) What level of interference do you observe at B?
(b) What happens if the frequency is lowered to f1=230 Hz?
(c) And to f2= 23Hz?

2. I guess, I have to calculate the periphery of the circle with given R, and hence divide Δx with λ, which would give me n. If its closer to a whole number, it would result in a constructive interference. With questions (b) and (c), my guess is, that it does not change the level of interference, since 230 and 23 are multiple integers of 2300 (factor 10).

 

[BvU]

Hello Jean, and welcome to PF.

Well, what do you find under (a)? What's against showing your results ?
And for (b) and (c) I wouldn't guess, but either see that yes, it is as you suspect, or no, factors of 10 can make a considerable difference!

 

[somegirl]

can u guys help me pls?
i got an exam tomorrov and I really need your help!
When the sound goes from surface to another(for example from water to air) what satys the same
a)period b)amplituda c) elongacioni d) frekuenc

 

[BvU]

http://www.passmyexams.co.uk/GCSE/physics/sound-waves.html

 

[HalfLostAndSearching]

I would like to provide a more detailed and accurate response to the content provided. The interference of sound waves in a circular tube is a phenomenon that occurs when two or more sound waves with the same frequency intersect each other, resulting in either a reinforcement or cancellation of the sound wave.

In this scenario, a sound wave with a frequency of 2300Hz is being sent into a circular tube with a radius of 160cm through an opening at point A. This sound wave will travel along the tube in both directions towards point B, where a receiver is located at an angle of 130° from point A. The speed of sound in air, which is an important factor in determining the level of interference, is given as 330 m/s.

(a) The level of interference observed at point B will depend on the relative phase of the two sound waves at that point. If the two sound waves arrive at point B in phase (constructive interference), the resulting sound wave will have a higher amplitude and therefore a higher intensity. On the other hand, if the two sound waves arrive out of phase (destructive interference), the resulting sound wave will have a lower amplitude and intensity. The exact level of interference can be calculated using the formula I = I1 + I2 + 2√(I1I2)cos(φ), where I1 and I2 are the intensities of the two sound waves and φ is the phase difference between them.

(b) If the frequency is lowered to 230Hz, the level of interference at point B will not change significantly as 230Hz is still a multiple of 2300Hz. This means that the two sound waves will still have the same phase relationship and will result in similar levels of interference.

(c) However, if the frequency is further lowered to 23Hz, the level of interference at point B will change significantly. This is because 23Hz is no longer a multiple of 2300Hz, and the two sound waves will have a different phase relationship, resulting in a different level of interference.

In order to accurately determine the level of interference, it is important to consider the wavelength (λ) of the sound waves in addition to the frequency. As mentioned in the content, the wavelength can be calculated by dividing the circumference of the circular tube (2πR) by the number of wavelengths (n) present in that circumference. This will help in determining the phase relationship between the two