Question

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 1

distance between two points having phase difference 5.6 rad is

Φ = 2.33 m

Step-by-step explanation:

given

frequency, f = 130Hz

speed of sound in air, v = 340m/s

distance between two crust or through with phase difference 2
`\pi` = λ (wavelength)

phase difference = 5.6 rad

note: distance between two points having a phase difference =
`( \lambda )/(2\pi )`

∴ distance between two points having phase difference of 5.6 rad is =
`( \lambda )/(2\pi )` ×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 =
`( 2.615 )/(2\pi )` ×5.6 = 2.33 m