The displacement of a standing wave on a string is given by D =2.4sin(0.70 x )co

Question

The displacement of a standing wave on a string is given by D=2.4sin(0.70x)cos(45t), where xand 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=2.40cm when t=2.3s.

Express your answer using two significant figures.

Explanation / Answer

given displacement of a standing wave on a string

D = 2.4sin(0.7x)cos(45t)

B. given that this is a standing wave

let the individual waves be Asin(kx - wt) , Asin(kx + wt)

then resultant amplitude = 2A

hence 2A = 2.4

A = 1.2

C. resultant frequency = w

hence frequency of the individual waves = 45 rad/s ( angular freq)

freq = w/2pi = 7.1619 hz

D. speed of waves = k*w = 0.7*45 = 31.5 cm/s

E. at x = 2.4 cm, t = 2.3 s

d(D)/dt = 2.4sin(0.7x)sin(45t)*(-45) = -108sin(0.7*2.4)sin(45*2.3)

speed = 18.433 m/s

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