Find the wavelength of the sound.

[alevis]

Two speakers , each producing a pure tone of 1000Hz, are separated by 4m and are placed against one wall of a 15m wide room. You walk along the opposite wall of the room and hear the locations of the maxima and minima interference patterns

a.)Find the wavelength of the sound.
b.)Find the total separation distance between the -4 and the +4 maxima and minima locations.
c.)If you slowly walk at 0.45m/s, find the amount of time to walk between the locations in part b.

 

[Redbelly98]

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(From https://www.physicsforums.com/showthread.php?t=5374 )

 

[nlightner]

a) The wavelength of the sound can be calculated using the formula λ = v/f, where λ is the wavelength, v is the speed of sound (approximately 343 m/s at room temperature), and f is the frequency. In this case, since the frequency is 1000Hz, the wavelength would be 343/1000 = 0.343m.

b) The total separation distance between the -4 and +4 maxima and minima locations can be calculated by multiplying the wavelength by the number of cycles between the two locations. In this case, there is a total of 8 cycles (4 maxima and 4 minima), so the total separation distance would be 0.343m x 8 = 2.744m.

c) To find the amount of time to walk between the locations in part b, we can use the formula t = d/v, where t is the time, d is the distance, and v is the speed. In this case, the distance is 2.744m and the speed is 0.45m/s, so the time would be 2.744/0.45 = 6.097 seconds. This means it would take approximately 6 seconds to walk between the -4 and +4 maxima and minima locations.