Physics · Waves · NEET
No. Plain wave number = 1/lambda and tells you how many complete waves fit in one metre, so its unit is per metre (m^-1). Angular wave number k = 2pi/lambda and tells you how much phase, in radians, the wave gains per metre, so its unit is rad/m. They differ by a factor of 2pi: k = 2pi x (wave number). In the NEET wave equation y = a sin(kx - wt), the symbol k is always the ANGULAR wave number (2pi/lambda), never the plain 1/lambda.
One full wavelength is one full cycle, and one full cycle is 2pi radians of phase. Plain wave number just counts cycles per metre (no 2pi). Angular wave number counts radians of phase per metre, and since each cycle is 2pi radians, you multiply by 2pi. That is exactly why k = 2pi/lambda while the plain wave number is 1/lambda.
It is the angular wave number, k = 2pi/lambda, with unit rad/m. Its partner in the time part is omega = 2pi/T (angular frequency). Both carry a 2pi because sine and cosine work in radians. From a given equation you read k as the number multiplying x, then get wavelength from lambda = 2pi/k.
Rearrange k = 2pi/lambda to lambda = 2pi/k. Example: if k = 5 rad/m, then lambda = 2pi/5 = 1.256 m. But watch the equation format: if it is written as y = a cos[2pi(...x...)], the number multiplying x is the PLAIN wave number 1/lambda, so lambda = 1/(that number). Reading the format correctly is where most students lose the mark.
NCERT calls the ANGULAR wave number k the propagation constant, with SI unit radian per metre (rad/m), defined as k = 2pi/lambda. The plain wave number 1/lambda is a separate quantity often used in spectroscopy. For NEET Waves, when you see 'k', assume it is the angular wave number unless the equation clearly shows a 2pi factored outside the bracket.
For a travelling harmonic wave y(x, t) = 2.0 cos[2pi(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.
k = 2pi x (plain wave number) = 2pi/lambda, while plain wave number = 1/lambda. So angular wave number is always 2pi times the plain wave number.
Plain wave number: per metre (m^-1). Angular wave number k: radian per metre (rad/m). The word 'radian' flags the version that carries the 2pi.
Yes. Here k = 2pi/lambda is the angular wave number, matching omega = 2pi/T. Both carry 2pi because the sine argument must be in radians.
Look at the bracket. If 2pi is factored outside, like cos[2pi(...x...)], the x-coefficient is the plain wave number 1/lambda. If there is no outside 2pi, like sin(kx - wt), the x-coefficient is the angular wave number k = 2pi/lambda.
Phase difference uses dphi = k x dx with the ANGULAR wave number. If you use the plain wave number by mistake you lose the 2pi and get an answer 6.28 times too small, which is exactly a wrong NEET option placed to catch you.
