A wave is represented by an eqution `y=c_1sin(c_2x+c_3t)`. In which direction is the wave going? Assume that `c_1,c_2 and c_3` are all positive.

The equation of a wave travelling on a string is y=(0.10mm)sin[3.14m^-1)x+(314s^-1)t] . (a) In which direction does the wave travel ? (b) Find the wave speed, the wavelength and the frequency of the wave. (c) What is the maximum displacement and the maximum speed of a portion of the string ?

The equation of a wave travelling on a string stretched along the X-axis is given by y=Ae^(((-x)/(a) + (t)/(T))^(2) (a) Write the dimensions of A, a and T. (b) Find the wave speed. (c) In which direction is the wave travelling? (d) Where is the maximum of the pulse located at t =T and at t = 2T ?

The maximum electric field in a plane electromagnetic wave is 600 N C^-1 . The wave is going in the x-direction and the electric field is in the y- direction. Find the maximum magnetic field in the wave and its direction.

If direction cosines of a line are (1)/(c),(1)/(c),(1)/(c)," then. "

Consider two curves C_1:y =1/x and C_2.y=lnx on the xy plane. Let D_1 , denotes the region surrounded by C_1,C_2 and the line x = 1 and D_2 denotes the region surrounded by C_1, C_2 and the line x=a , Find the value of a

The differential equaiotn which represents the family of curves y=C_(1)e^(C_(2)x) , where C_(1) and C_(2) are arbitrary constants, is

Let y=1/(1+x^(2)) at t=0 s be the amplitude of the wave propogating in the positive x-direction. At t=2 s, the amplitude of the wave propogating becomes y=1/(1+(x-2)^(2)) . Assume that the shape of the wave does not change during propogation. The velocity of the wave is

If three lines whose equations are y = m_(1) x + c_(1) , y = m_(2) x + c_(2) " and " m_(3) x + c_(3) are concurrent, then show that m_(1) (c_(2) - c_(3)) + m_(2) (c_(3) - c_(1)) + m_(3) (c_(1) - c_(2)) = 0 .