Question

A periodic vibration at x = 0, t = 0 displaces air molecules along the x direction by smax = 3.1E-05 m. The motion produces a sound wave that travels at a velocity of v = 340 m/s with a frequency of f = 35 Hz. Take the density of air as rhoa = 1.20 kg/m3.

Answer 1

wavelength=9.71m

wave number=k=0.64/m

angular velocity ω=219.91rad/s

Step-by-step explanation:

A periodic vibration at x = 0, t = 0 displaces air molecules along the x direction by smax = 3.1E-05 m. The motion produces a sound wave that travels at a velocity of v = 340 m/s with a frequency of f = 35 Hz. Take the density of air as rhoa = 1.20 kg/m3.

Parameters are

density= 1.20 kg/m3.

smax=3.1E-05 m

frequency of f = 35 Hz.

velocity of v = 340 m/s

v=f*wavelength

340=35*wavelength

wavelength=9.71m

wave number k

k=
`2\pi /lambda`

k=2*3.14/9.71

k=0.64/m

Angular velocity

ω=
`2\pi f`

2*3.14*35

ω=219.91rad/s

Answer 2

Wavelength = 9.61m

Wave number = 0.65M-1

Angular frequency = 219.94rad/sec

Step-by-step explanation:

Wavelength= v/f

=340/35

= 9.71m

Wave number = 2π/wavelength

= 2*3.142/9.71

= 6.284/9.71

= 0.65M-1

Angular frequency = 2πf

= 2*3.142*35

= 219.94rad/sec