A loudspeaker at the origin emits a 130 Hz tone on a day when the speed of sound is 340 m/s. The phase difference between two points on the x-axis is 5.6 rad.What is the distance between these two points
A loudspeaker at the origin emits a 130 Hz tone on a day when the speed of sound is 340 m/s. The phase difference between two points on the x-axis is 5.6 rad.What is the distance between these two points
Answer:
distance between two points having phase difference 5.6 rad is
Φ = 2.33 m
Explanation:
given
frequency, f = 130Hz
speed of sound in air, v = 340m/s
distance between two crust or through with phase difference 2[tex]\pi[/tex] = λ
(wavelength)
phase difference = 5.6 rad
note: distance between two points having a phase difference = [tex]\frac{ \lambda }{2\pi }[/tex]
∴ distance between two points having phase difference of 5.6 rad is = [tex]\frac{ \lambda }{2\pi }[/tex] ×5.6
Recall
v = f × λ
speed = frequency × wavelength
wavelength = speed/frequency
λ = v/f
λ = 340/130 = 2.615 m
∴ distance between two points having phase difference 5.6 rad is = [tex]\frac{ 2.615 }{2\pi }[/tex] ×5.6 = 2.33 m