A progressive wave is represented by y=10Sin(1000?t??x34) y = 10 Sin ( 1000 ? t ? ? x 34 ) . two layers of the wave separated by 153cm have a phase differen...
A progressive wave is represented by y=10Sin(1000?t??x34) . two layers of the wave separated by 153cm have a phase difference of
Answer Details
The given wave equation is y = 10 sin(1000?t - ?x/34).
The general equation for a progressive wave is y = A sin(?t - ?x), where A is the amplitude, ? is the angular frequency, t is the time, x is the distance, and ? is the phase angle.
Comparing this with the given equation, we get:
A = 10
? = 1000
?x/34 = ?t
The wavelength (?x) of the wave is given by:
?x = (2?/?)
where ? is the wavelength and ? is the wave number.
The phase difference between two points separated by a distance d is given by:
? = (2?/?)d
where ? is the phase difference.
Let's find the wavelength of the wave:
?x = (2?/?) = (2?/1000) = 0.00628 m
The distance between the two layers of the wave is 153 cm = 1.53 m.
So, the number of wavelengths between the two layers of the wave is:
n = (1.53/0.00628) = 243.06
Since the two layers of the wave are separated by half a wavelength, the number of half-wavelengths is:
n/2 = 121.53
Therefore, the phase difference between the two layers of the wave is:
? = (2?/?)d = (2?/243.06)(1.53) = 0.398 rad = 22.8 degrees
Converting radians to degrees, we get:
22.8 × (180/? ) = 1307.6/?
None of the given options match this answer. Therefore, there is no correct option.