A wave is propagating along x-axis. The displacement of particles of the medium in Z-direction at t=0 is given by: z=exp[−(x+2)2] 'x' is in meters. At t=1s, the same wave disturbance is given by: z=exp[−(2−x)2]. Then, the wave propagation velocity is
A wave is propagating along x-axis. The displacement of particles of the medium in Z-direction at t=0 is given by: z=exp[−(x+2)2] 'x' is in meters. At t=1s, the same wave disturbance is given by: z=exp[−(2−x)2]. Then, the wave propagation velocity is
The correct option is A 4m/s in + x direction
The given equation of
wave: f(x)=z0=e−(x+2)2 ...........at
initial position.
Let the wave be travelling with a speed of "v"
Hence the speed at any time after "t" seconds is
given as:
f(x±vt)=zt=e−(x+2±vt)2 where
f(x+vt)= wave
travelling in negative z direction with speed "v"
f(x−vt)= wave travelling in positive z direction with speed "v"
Now equating this equation for time = 1 second
z1=e−(2−x)2.....1
Now equating this
for the general equation
z1=e−(x+2±v)2....2
Now equating 1 and 2
e−(2−x)2=e−(x+2±v)2
the above
two equations are equal when v=4 and "-" sign is taken that is
e−(2−x)2=e−(x+2−4)2
Hence the speed of the wave is 4m/s
and since the equation of the form f(x-vt) satisfies the given condition the
wave is travelling in the positive "z" direction
Hence option A is correct
The given equation of
wave: f(x)=z0=e−(x+2)2 ...........at
initial position.
Let the wave be travelling with a speed of "v"
Hence the speed at any time after "t" seconds is
given as:
f(x±vt)=zt=e−(x+2±vt)2 where
f(x+vt)= wave travelling in negative z direction with speed "v"
f(x−vt)= wave travelling in positive z direction with speed "v"
Now equating this equation for time = 1 second
z1=e−(2−x)2.....1
Now equating this for the general equation
z1=e−(x+2±v)2....2
Now equating 1 and 2
e−(2−x)2=e−(x+2±v)2
the above two equations are equal when v=4 and "-" sign is taken that is
e−(2−x)2=e−(x+2−4)2
Hence the speed of the wave is 4m/s and since the equation of the form f(x-vt) satisfies the given condition the wave is travelling in the positive "z" direction
Hence option A is correct
