Physics · Waves · NEET
Watch one point on the wave (say a crest). Its phase (kx - wt) must stay the same as time passes. As t increases, wt grows, so x must also grow to keep (kx - wt) constant. Growing x means the crest moves toward +x. So (kx - wt) = wave moving in the +x direction. Flip the sign to (kx + wt) and the wave moves in the -x direction. This sign is the single most common way NEET asks you to identify direction.
a = amplitude, the maximum displacement of a particle from rest (metres). k = angular wave number = 2 pi / lambda, unit rad/m — it is the number that multiplies x. w (omega) = angular frequency = 2 pi / T = 2 pi f, unit rad/s — it is the number that multiplies t. From an equation you read k and w straight off, then get lambda = 2 pi / k and f = w / (2 pi).
No. y is the displacement of a particle at position x and time t — it changes every instant between +a and -a. 'a' is fixed: it is only the biggest value y can reach. Confusing the two is a classic slip. y = a only at the moment sin(...) = 1.
phi is the initial phase — it tells you the starting displacement at x = 0, t = 0. It just shifts the wave sideways in time; it does not change amplitude, wavelength or frequency. In many NEET problems phi = 0, but if the equation gives an extra constant inside the bracket, that is phi and you can ignore it when finding a, k, w.
Both describe a wave moving in +x, because sin(wt - kx) = -sin(kx - wt), which is just a phase flip of pi (an upside-down but identical travelling wave). What actually decides direction is whether x and t carry the SAME sign or OPPOSITE signs inside the bracket. Opposite signs (like kx - wt) = +x direction; same signs (like kx + wt) = -x direction.
For a travelling harmonic wave y(x, t) = 2.0 cos[2 pi (10t - 0.0080x + 0.35)], where x and y are in cm and t in s, the phase difference between the oscillatory motion of two points separated by 0.5 m is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
A progressive (or travelling) wave is a disturbance that moves through a medium carrying energy forward, while the particles of the medium only oscillate about fixed positions. Its displacement is described by y = a sin(kx - wt + phi).
radian per metre (rad/m), often written as m^-1. It is defined as k = 2 pi / lambda.
Wave speed v = w / k, which is the same as v = f x lambda. Just read w (coefficient of t) and k (coefficient of x) from the equation and divide.
Either is fine — sin and cos differ only by a phase of pi/2, so both describe the same physical wave with a different starting point. NCERT uses sine as standard; NEET questions may give cosine (as in the 2026 PYQ).
It means the particle at x = 0 has zero displacement at t = 0 and is about to move in the positive direction. It is the simplest choice and is assumed in most textbook forms.
