For the transverse wave with displacement y8m sin2 pi1m x 4

For the transverse wave with displacement y=8m sin(2 pi/1m x + 4 pi/1s t) what is the wavespeed in meters/second? For the transverse wave with displacement y=8m sin(2 pi/1m x + 4 pi/1s t) what is the magnitude of the largest transverse velocity in meters/second? For the transverse wave with displacement y=8m sin(2 pi/1m x + 4 pi/1s t) what is the magnitude of the displacement at x=0.5m and time t=0.5s in meters? For the transverse wiive with displacement y=8m sin(2 pi/1m x + 4 pi/1s t) with tension 2N, what is the linear mass density, mu, in kilograms/meter? Two waves of amplitude lm that are equal in every way have a phase difference (relative phase) of pi/3 radians, what is the amplitude of the superposition of the two waves in meters? A string has two ends 2 meters apart that are fixed, it\'s tension is 5 Newtons, it\'s mass density is 3grams/meter what is the frequency (in Hertz) that corresponds to the largest wavelength?

Solution

a)

Compare the given wave equation with

Y=ASin(Kx-Wt)

Amplitude A=8 m

Wave number K=2pi

Since K=2pi/lambda

=>lambda =2pi/2pi =1 m

angular frequency W=4pi rad/s

since f=W/2pi =4pi/2pi =2 Hz

Wave speed

V=f*lambda =2*1 =2 m/s

b)

Maximum transverse velocity

V_max=AW =8*4pi

V_max = 100.53 m/s

c)

Y=8Sin(2pi*0.5+4pi*0.5)

Y=0 m

d)

Since

V=sqrt[T/u]

Linear mass density

u=T/V² = 2/2² =0.5 kg/m