VERY HARD PHYSICS PROBLEM

The vertical displacement of a wave on a string is described by the equation y(x,t)=Asin(Bx-Ct), in which A, B, and C are positive constants.


Does this wave propagate in the positive or negative x direction?
What is the wavelength of this wave? (Use Variables)
What is the frequency of this wave? (Use Variables)
What is the smallest positive value of x where the displacement of this wave is zero at t=0?




thanks

Hello friend Jordy, recall the general form of a progressive wave y(x,t) = a sin 2pi(t/T - x//\)
The wave propagates in the positive X direction.
To get wavelength we equate -2pi x/ /\ = Bx (Here we have to take only magnitudes)
Hence /\ = 2 pi/ B
TO get frequency equating 2 pi t/T = -Ct
we get 1/T = C/2pi
HEnce the frequency = C / 2 pi
The smallest positve value of x for the displacement to be zero is /\ /2 ie half wavelength.

If you think this is hard, wait till you get to superpositioning.

Wavelength:
B = 2pi/λ
So λ = (2pi)B

Frequency:
C = 2pi/T = (2pi)f
So f = C/(2pi)

In case you didn't know, B is known as the wave number, and C is known as the angular frequency.

If t = 0, then you have:
Asin(Bx)
If you want the displacement to be zero, set this equation to zero.
Asin(Bx) = 0.
x = 0.