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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

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4 votes

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.

User Tortuga
by
8.1k points
5 votes
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

User Amit Kotha
by
7.2k points