A transverse wave travelling along a string has a form y=0.3sin pi (0.5z-50t) : obtain the wave length, 1. wave number, frequency, period and phase velocity ?
2. find the max-transverse speed of any particle in the string. relate y=0.3sin pi (0.5z-50t) to y=asin(kz-wt) and y= acos(-kz-cot)

0.5, 25/pi Hz, pi/25 seconds, 100 m/s

Explanation:

y=0.3sin pi (0.5z-50t)

wave number (k) = 0.5

2pift = 50t

f = 50/2pi

f= 25/pi Hz

T = 1/f = 1 ÷ 25/pi

T = pi/25 seconds

2pi/lamda = 0.5

lamda = 2pi/0.5

lamda = 4pi m

Velocity = frequency*wavelength

= 25/pi × 4pi

= 100 m/s

answer; john stuart mill's principle of utility is your answer; /// good luck

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