The displacement of a standing wave on a string is given by D = 3.6sin(0.53 x )c

Question

The displacement of a standing wave on a string is given by D= 3.6sin(0.53x)cos(45t), where x and D are in centimeters and t is in seconds.

Part B

Give the amplitude of each of the component waves.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Part C

Give the frequency of each of the component waves.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

?

Part D

Give the speed of each of the component waves.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Part E

Find the speed of a particle of the string at x=2.80cm when t=2.3s.

Express your answer using two significant figures.

Explanation / Answer

D = 3.6sin(0.53x)cos(45t)

D = 1.8* 2*sin(theta) cos(alpha)

D = 1.8sin(0.53x+45t)+1.8sin(0.53x-45t)

Part B:

Amplitudes are 1.80 cm and 1.80 cm.

A1,A2 = 1.80,1.80

Part C:

Both wave will have equal frequency and the value of frequency is:

f = omega/2pi = 45/(2pi) = 7.16 Hz.

f1,f2 = 7.16,7.16

Part D:

Speed of the waves = omega/k = 45/0.53 = 84.91 cm/s

v1,v2 = 84.91,84.91

Part E:

speed of the particle = D/t = -45*3.6sin(0.53x)sin(45t)

at (2.80cm,2.3s),  D/t = -45*3.6*sin(0.53*2.80)*sin(45*2.3)

v = -27.71 cm/s

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