A plane sound wave propagated in air has individual particles which execute a periodic motion such that their displacement y from their rest position at any time t is y=5x10^(-6)sin(800pie(t)+theta). Calculate (i) wavelength. (ii) phase diff in degree between particles 17cm apart.

y =A sin (800 pi t + Th)

when t = 0, 800 pi t = 0
so when 800 pi t = 2 pi
we have done a full cycle.
800 pi T = 2 pi
T = 1/400 second
use velocity of sound now to get
wavelength L = distance = rate * time =(1/400)(velocity of sound)

once you have L
.17 meters /L = fraction of wavelength = fraction of circle/360

you tried but compare the equation with y=asin(2pieft-2piex/Λ)

f-frequency
t-time
Λ-wavelength
by comparing you will solve it easily

To calculate the wavelength and phase difference between particles in the given scenario, we need to understand the equation of the wave and use the relevant formulas.

The equation of the wave is given as: y = 5x10^(-6)sin(800πe(t) + θ)

(i) Wavelength (λ):
The general equation for a plane wave is given as: y = A*sin(kx - ωt + θ)

Comparing this equation with the given equation, we can find the value of k, which will help us calculate the wavelength (λ).

In the given equation, k = 800πe
We know that k = 2π/λ

Rearranging the equation, we have: λ = 2π/k

Substituting the value of k from the given equation, we get: λ = 2π/(800πe)
Simplifying, we find: λ ≈ 1/(400e) meters

(ii) Phase Difference in degrees between particles 17 cm apart:
To calculate the phase difference, we need to find the difference in the phase angles (θ) between two particles that are 17 cm apart.

The phase angle term in the equation is given as: θ = 800πe(t)

Let's find the phase difference (Δθ) between two particles that are 17 cm apart (or 0.17 meters).

The phase difference can be calculated using the formula: Δθ = 2πΔx/λ

Where Δx represents the difference in position of the particles and λ is the wavelength.

Substituting the values, we have: Δθ = 2π * 0.17 / (1/(400e))
Simplifying, we find: Δθ ≈ 2738 radians

To convert this into degrees, we multiply by 180/π:
Δθ (in degrees) ≈ 2738 * 180/π ≈ 156880 degrees

Therefore, the phase difference in degrees between particles 17 cm apart is approximately 156880 degrees.