Question

Consider the waves represented by the following functions. (a) y = 4 sin (3x − 15t) (b) y = 6 cos (3x + 15t − 2) (c) y = 8 sin (2x + 15t) (d) y = 8 cos (4x + 20t) (e) y = 7 sin (6x − 24t) Rank the waves represented by the above functions from the largest to the smallest according to the following conditions. (Use only ">" or "=" symbols. Do not include any spaces or parenthesis around the letters or symbols.) (i) their amplitudes (ii) their wavelengths (iii) their frequencies (iv) their periods (v) their speeds

Answer 1

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.

Answer 2

Rank the waves represented by the above functions from the largest to the smallest according to the following conditions. (Use only ">" or "=" symbols. Do not include any spaces or parenthesis around the letters or symbols.)

(i) their amplitudes





(ii) their wavelengths





(iii) their frequencies





(iv) their periods





(v) their speeds