Q.A transverse wave moves from a medium A to a medium B. In medium A, the velocity of the transverse wave is 500 m s$^{-1}$ and the wavelength is 5 m. The frequency and the wavelength of the wave in medium B when its velocity is 600 m s$^{-1}$, respectively are

A set of precise terms is needed to compare and distinguish any two wave patterns quantitatively. For a transverse wave, the crest is the highest point of the disturbance above the undisturbed (mean) reference level, and the trough is the lowest point below it; for a longitudinal wave the analogous features are the compression (crowded, high-pressure region) and rarefaction (spread-out, low-pressure region). The wavelength $\lambda$ (SI unit: metre) is the length of one complete, non-repeating section of the wave pattern -- for a transverse wave, the distance between two consecutive crests (or two consecutive troughs); for a longitudinal wave, the distance between two consecutive compressions (or two consecutive rarefactions). The frequency $f$ (SI unit: hertz, Hz) is the number of complete waves that cross a fixed point per second, while the time period $T$ (SI unit: second) is the time taken for exactly one wave to cross that point; because one wave crossing takes $1/f$ seconds, frequency and period are reciprocals of each other, $T = 1/f$. The amplitude $A$ of a wave is the maximum displacement of the medium from its mean (reference) position -- essentially the height of a crest or the depth of a trough measured from the undisturbed level -- and it is amplitude alone, not wavelength, frequency or wave speed, that distinguishes two otherwise-identical sinusoidal waves of different "size". The wave (or phase) velocity $v$ is the distance the wave pattern itself advances in one second, and combining the definitions above gives the fundamental wave relation $v = f\lambda$ (also written $v = \lambda/T$): a wave with a higher frequency necessarily has a proportionally shorter wavelength for the same speed, and vice versa, so their product -- the speed -- stays fixed for a given medium. Two further quantities restate the same physics in angular form: the angular frequency $\omega = 2\pi/T = 2\pi f$ (unit rad/s) counts radians of phase swept out per second, and the (angular) wave number $k = 2\pi/\lambda$ (unit rad/m) counts radians of phase packed into each metre of the wave pattern; combining these reproduces the same speed relation as $v = \omega/k$.