Final answer:
Ranking the waves based on their amplitudes, wavelengths, frequencies, periods, and speeds.
Step-by-step explanation:
Ranking the waves:
(i) Amplitudes: Wave (d) y = 8 cos (4x + 20t) > Wave (c) y = 8 sin (2x + 15t) > Waves (a) y = 4 sin (3x − 15t) and (e) y = 7 sin (6x − 24t) > Wave (b) y = 6 cos (3x + 15t − 2)
(ii) Wavelengths: Wave (e) y = 7 sin (6x − 24t) > Wave (c) y = 8 sin (2x + 15t) > Wave (d) y = 8 cos (4x + 20t) > Wave (a) y = 4 sin (3x − 15t) = Wave (b) y = 6 cos (3x + 15t − 2)
(iii) Frequencies: Wave (e) y = 7 sin (6x − 24t) > Wave (b) y = 6 cos (3x + 15t − 2) > Wave (a) y = 4 sin (3x − 15t) > Wave (c) y = 8 sin (2x + 15t) = Wave (d) y = 8 cos (4x + 20t)
(iv) Periods: Wave (e) y = 7 sin (6x − 24t) > Wave (b) y = 6 cos (3x + 15t − 2) > Wave (a) y = 4 sin (3x − 15t) > Wave (c) y = 8 sin (2x + 15t) = Wave (d) y = 8 cos (4x + 20t)
(v) Speeds: All waves have the same speed since the coefficient of t in each wave function is the same.