A 3.kHz tone is made by a speaker with a diameter of .175m. The temp warms from

Question

A 3.kHz tone is made by a speaker with a diameter of .175m. The temp warms from 0 t 29 degrees Celcius. If airis an ideal gas, what is the chane in the diffraction angle? I don't understand how temp affects the angle, or how to dothis problem, Please help. A 3.kHz tone is made by a speaker with a diameter of .175m. The temp warms from 0 t 29 degrees Celcius. If airis an ideal gas, what is the chane in the diffraction angle? I don't understand how temp affects the angle, or how to dothis problem, Please help.

Explanation / Answer

we have at 00C the speed of sound is air is given as 331m/s .This corresponds to a wavelength of 1 = v/f        = 331m/s /3.0*103Hz        = 0.1103m the diffraction angle is      1 =sin-1(1.22/D)            =sin-1(1.22*0.1103m/0.175m)            =50.30 the speed of sound at 290C is      v = (331m/s)*(302K/273K)         = 348m/s the wavelength at this temperature is       2 = 348m/s /3.0*103Hz            = 0.116m the diffraction angle is      1 =sin-1(1.22/D)            =sin-1(1.22*0.116m/0.175m)            =540 the change in the diffraction angle is thus = 540 - 50.30         =3.70 the speed of sound at 290C is      v = (331m/s)*(302K/273K)         = 348m/s the wavelength at this temperature is       2 = 348m/s /3.0*103Hz            = 0.116m the diffraction angle is      1 =sin-1(1.22/D)            =sin-1(1.22*0.116m/0.175m)            =540 the change in the diffraction angle is thus = 540 - 50.30         =3.70

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