The wave function for a traveling wave on a taut string is (in St unit

Jason Yuhas

Jason Yuhas

Answered question

2021-12-17

The wave function for a traveling wave on a taut string is (in St units)
y(x,t)=0.300sin(13πt2πx+π4)
(а) What are the sреed and direction of travel of the wave?
speed _ m/s
direction Select
(b) what is the vertical position of an element of the string at t=0,x=0.170m?
(с) what is the wavelength of the wave?
(d) what is the frequency of the wave?
(е) What is the maximum transverse spеed of an element of the string?

Answer & Explanation

eninsala06

eninsala06

Beginner2021-12-18Added 37 answers

Step 1
Wave Junction of a travellind wave,
y(x,t)=0.300sin(13πt2πx+π4) (1)
This is the equation of wave showing its propagation with the position 4 time.
This is a sinusoidal wave.
Step 2
The general equation of trevellind wave
y(x,t)=Asin(ωtkx+ϕ) (2)
On company (1)+(2)
A(Amplitude)=03m
a) speed of the wave, v=ωk=13π2π
V=6.5msec In general equation, y=Asin(±ωt±kx+ϕ)
If they some sign, then wave move '-' x direction + if they have differents sign, then wave move in '+' x direсtion
In equation diven, they have different sign (+ωt,kx), so direction of wave is in position x direction

Neunassauk8

Neunassauk8

Beginner2021-12-19Added 30 answers

b)
y=0.3sin(13πt2πx+π4)
At t=0,+x=0.170m
y=0.3sin(13π×02π×0.170+π4)
=0.3sin(0.09π)
y=0.003m
nick1337

nick1337

Expert2021-12-27Added 777 answers

c)
k=2πλ
given k=2π,2π=2πλ
λ=1m
d)
ω=13π
2πf=13π
f=6.5Hr

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