The tension in a string is 16 N, and its linear density is 0.77 kg/m. A wave on

Question

The tension in a string is 16 N, and its linear density is 0.77 kg/m. A wave on the string travels toward the -x direction; it has an amplitude of 3.8 cm and a frequency of 13 Hz.
(a) What is the speed of the wave? (Give your answer to two significant figures.)
_______m/s
(b) What is the wavelength of the wave? (Give your answer to two significant figures.)
_______m

(c) Write down a mathematical expression (like the following equations) for the wave.
y = A sin
2pft - 2px
?

y = A sin
2pft + 2px
?

Substitute numbers for the variables A, f, and ?. (Use the following as necessary: x and t. Assume x is in meters and t is in seconds.)
y = ____ m

Explanation / Answer

The tension in a string is 16 N, and its linear density is 0.77 kg/m. A wave on the string travels toward the -x direction; it has an amplitude of 3.8 cm and a frequency of 13 Hz.
Given that Tension in a string is T = 16.0 N linear density = 0.77 kg/m Amplitude A =3.8 x 10^-2 m frequency f = 13 Hz .------------------------------------------------------ a) The speed of the wave is            v = [T/]               = [(16.0 N)/(0.77 kg/m)]               = 4.558 m/s b) The wavelength of the wave is               = v/f                  = (4.558 m/s)/(13.0 Hz)                 = 0.35 m c) The displacement of the wave is      y = A sin (kx + t)           Here k = 2/ = 2/(0.35 m) = 17.95 /m          =2 f = 2(13.0 Hz) = 81.68rad/s      y = (3.8 x 10^-2 m) sin [(17.95 rad/m) x+ ( 81.68rad/s)t]      y = (3.8 x 10^-2 m) sin [(17.95 rad/m) x+ ( 81.68rad/s)t]

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