Final answer:
The sinusoidal wave created by the cousin has an amplitude of 0.075 m, angular frequency of 12.57 rad/s, a period of 0.50 s, a wavelength of 6.0 m, and a wave number of 1.05 m⁻¹.
Step-by-step explanation:
To find the characteristics of the sinusoidal wave that the cousin creates we need to analyze the given parameters and apply our understanding of wave mechanics.
Finding Amplitude, Angular Frequency, Period, Wavelength, and Wave Number
Amplitude (A): It is given as 0.075 m.
Angular Frequency (\( \omega \)):
It can be found using the formula \( \omega = 2\pi f \), where frequency (f) is 2.00 Hz.
Therefore, \( \omega = 2\pi \times 2.00 \) Hz = 12.57 rad/s.
Period (T): The period is the inverse of the frequency.
\( T = \frac{1}{f}
= \frac{1}{2.00} \) s
= 0.50 s.
Wavelength (\( \lambda \)):
It can be calculated using the wave velocity (v) and frequency with the formula \( \lambda = \frac{v}{f} \).
Given v = 12.0 m/s, and f = 2.00 Hz, \( \lambda = \frac{12.0}{2.00} \) m = 6.0 m.
Wave Number (k):\( k = \frac{2\pi}{\lambda} \),
so \( k = \frac{2\pi}{6.0} \) m⁻¹
= 1.05 m⁻¹.
The wave that the cousin is creating on the clothesline has an amplitude of 0.075 m, angular frequency of 12.57 rad/s, a period of 0.50 s, a wavelength of 6.0 m, and a wave number of 1.05 m⁻¹.