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.

Two waves are represented by: y_(1)=4sin404 pit and y_(2)=3sin400 pit . Then :

C_1 is a curve y^2=4x,C_2 is curve obtained by rotating C_1,120^@ in anti -clockwise direction C_3 is reflection of C_2 with respect to y=x and S_1,S_2,S_3 are foci of C_1,C_2 and C_3 , respectively, where O is origin. If (t^2,2t) are parametric form of curve C_1 , then the parametric form of curve C_2 is

C_1 is a curve y^2=4x,C_2 is curve obtained by rotating C_1,120^@ in anti -clockwise direction C_3 is reflection of C_2 with respect to y=x and S_1,S_2,S_3 are foci of C_1,C_2 and C_3 , respectively, where O is origin. IF S_1(x_1,y_1),S_2(x_2,y_2) and S_3(x_3,y_3) then the value of sumx_1^2+sumy_1^2 is

C_1 is a curve y^2=4x,C_2 is curve obtained by rotating C_1,120^@ in anti -clockwise direction C_3 is reflection of C_2 with respect to y=x and S_1,S_2,S_3 are foci of C_1,C_2 and C_3 , respectively, where O is origin. Area of DeltaOS_2S_3 is

The differential equation which represents the family of curves y=c_(1)e^(c_(2^(x) where c_(1)andc_(2) are arbitary constants is

Given below are some functions of x and to represent the displacement of an elastic wave. (i) y = 5 cos (4x) sin (20t) (ii) y = 4 sin (5x - (t)/(2)) + 3 cos (5x - (t)/(2)) (iii) y = 10 cos {(252 -250)pi t] cos {(252 +250)pi t] (iv) y = 100 cos (100 pi t + 0.5 x) State which of these represent (a) a travelling wave along-x direction (b) a stationary wave (c) beats (d) a travelling wave along + x direction. Give reasons for your answers.

A transverse harmonic wave on a string is described by y(x,t) = 3.0 sin (36 t + 0.018x + pi//4) where x and y are in cm and t in s. The positive direction of x is from left to right (a) Is this a travelling wave or a stationary wave? If it is travelling what are the speed and direction of its propagation? (b) What are its amplitude and frequency? (c ) What is the initial phase at the origin ? (d) What is the least distance between two successive crests in the wave?

The transverse displacement of a string (clamped at its both ends) is given by y(x, t) = 0.06 sin ((2 x)/(3) x) cos (120 pi t) where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 xx 10^(-2) kg . Answer the following : (a) Does the function represent a travelling wave or a stationary wave? (b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency , and speed of each wave ? (c ) Determine the tension in the string.

If three lines whose equations are y=m_(1) x+c_(1), y=m_(2) x + c_(2) and y=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 .