A sinusoidal transverse wave is traveling along a string in the negative directi

Question

A sinusoidal transverse wave is traveling along a string in the negative direction of an x axis. The figure below shows a plot of the displacement as a function of position at time t = 0. The x axis is marked in increments of 10 cm and the y axis is marked in increments of 2.5 cm. The string tension is 4.7 N, and its linear density is 16 g/m.

(a) Find the amplitude.
m

(b) Find the wavelength.
m

(c) Find the wave speed.
m/s

(d) Find the period of the wave.
s

(e) Find the maximum speed of a particle in the string.
m/s

(f) Complete the equation describing the traveling wave, in which x and y are in meters, angle in radians, and t is in seconds.

y(x, t) =  sin

  x +  t +

Explanation / Answer

as per chegg guidelines 4 subparts can be answered

a)

Amplitude

A=12.5 cm

b)

wavelength

lambda =distance between two successive crests

lambda =40 cm

c)

Wave speed

V=sqrt[T/u]=sqrt[4.7/0.016]

V=17.14 m/s

d)

Period of the wave

T=lambda V=0.4/17.14

T=0.023338 s

e)

W=2pi/T =2pi/0.023338

W=269.22 rad/s

Maximum speed

Vmax=AW=0.125*269.22

Vmax=33.65 m/s

f)

Wave number

K=2pi/lambda =2pi/0.4 =15.708 m-1

at X=0 ,t=0

10 =12Sin(o)

o=56.44o*(pi/180) =0.985 rad

Y(x,t) =(12.5 cm)Sin[(15.808 m-1)x +(269.22 rad/s)t+(0.985 rad)]

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