A wave is represented by the equation y=2sin(0.5x-200t), when all distances are measured in centimeters and time in seconds.For this wave calculate its wavelength,frequency and speed.
Answers
A wave is represented by the equation, y = 2sin(0.5x - 200t)
on comparing with y = Asin(kx - ωt)
we get, A = 2 , k = 0.5 and ω = 200
here, A is amplitude, k is phase constant. and ω is angular frequency.
so, k = 2π/λ = 0.5
or, λ = 4π cm
frequency , f = ω/2π
= 200/2π = 100/π ≈ 32 Hz
now, speed of wave = wavelength × frequency
= 4π cm× 100/π = 400 cm/s = 4m/s
so, wavelength = 4π cm
frequency = 100/π or, 32Hz
speed = 4 m/s
Answer:frequency (100Hz)
Wave length (4m)
Speed (400m/s)
Explanation:y = 2 sin ( 0.5x - 200t) compare to y = A sin 2 pie ÷ wave length (x-vt)
Yes = A sin (2x ÷ wavelength - 2vt ÷ wavelength)----------equation (i)
Yes = 2 sin pie ( 0.5x - 200t)----equation (ii)
from equation (ii), 0.5x = 2x ÷ wavelength in equation (i)
0.5x X wavelength = 2x
Wavelength = 2x ÷ 0.5x
wavelength = 4m
From equation (ii), 200t = 2vt ÷ wavelength in equation (i)
200t X wavelength = 2vt
substitute wavelength = 4 above
200t X 4 = 2vt
(200t X 4) ÷ 2t = v
v = (200 X 4) ÷ 2
v = 800 ÷ 2
v = 400m/s
From v = wavelength X frequency, frequency (f) = v ÷ wavelength
= 400 ÷ 4
= 100Hz
:. f = 100Hz, wavelength = 4m, v = 400m/s