Question

The transverse displacement of a stretched string from equilibrium as a function of time and position is given by:
y=0.13 cos(3 x + 54 t). x and y are in m; t is in s.
True False Greater than Less than Equal to  The wavelength is ..... 1 m.
True False Greater than Less than Equal to  The speed of the wave is ..... 17 m/s.
True False Greater than Less than Equal to  The period is ..... 0.1 seconds.
True False Greater than Less than Equal to  The wave travels in the negative x direction.

A traveling wave can be any function of (2*pi*x/lamda-2*pi*t/period). Calculate the various parameters where needed then select the proper answers.

Incorrect.

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Calculate the average power transmitted by the string. Data: mass of a 177 m long piece of the string is 1.47 kg.

Answer 1

The transverse displacement of a stretched string from equilibrium as a function of time and position is given by:

y = 0.13 cos(3x + 54t) where x and y are in meters t is in seconds.

From the eqn, we get:

k = 3, w = 54, A = 0.13

(1) The wavelength is Greater than 1m

λ = 2pi/k = 2*3.1416/3 = 2.0944 m > 1

(2) The speed of the wave is greater than 17 m/s

v = w/k = 54/3 = 18 m/s

(3) The period is Greater than 0.1 s

T = 2pi/w = 2*3.1416/54 = 0.1164 s > 0.1

(4) The wave travels in the negative x direction True

A traveling wave can be any function of (2*pi*x/lamda-2*pi*t/period).True

Calculate the various parameters where needed then select the proper answers.

Then... Calculate the average power transmitted by the string. Data: mass of a 177 m long piece of the string is 1.47 kg

m/L = 1.47/177 = 0.008305 kg/m

E/cycle = 0.5*m/L*omega^2*A^2*wavelength

= 0.5 * 0.008305*54*54*0.13*0.13*2.0944 = 0.4286 J/cycle

P = E/cycle*f = 0.5*m/L*omega^2*A^2*wave velocity

= 0.5 * 0.008305*54*54*0.13*0.13* 18 = 3.68 W

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