A harmonic wave with a frequency and an amplitude

[Ammar2211]

Homework Statement

A harmonic wave with a frequency of 80Hz and an amplitude of 0.025m travels along a string to the right with a speed of 12m/s.
a) Write a suitable wave function for this wave.
b) Find the maximum speed of a point on the string.
c) Find the maximum acceleration of a point on the string.

Relevant Equations

y = f(x) = ASin(2πft + ϕ)

y(x,t)−y0=Asin(2πft±2πx/λ+ϕ)

For part (a), which generic function would be used? either y = f(x) = ASin(2πft + ϕ) or y(x,t)−y0=Asin(2πft±2πx/λ+ϕ) ??

Furthermore how to find out max. speed & max. acceleration of a point on the string?? Any directions please

 

[PeroK]

For part (a), which generic function would be used? either y = f(x) = ASin(2πft + ϕ) or y(x,t)−y0=Asin(2πft±2πx/λ+ϕ) ??

Furthermore how to find out max. speed & max. acceleration of a point on the string?? Any directions please

A wave function must be a function of both $x$ and $t$. To say $f(x) = \sin(2\pi f t)$ doesn't make mathematical sense. Your second equation is correct.

For parts b) and c), what does the wave motion consist of in terms of the motion of the string?

 

[Ammar2211]

A wave function must be a function of both $x$ and $t$. To say $f(x) = \sin(2\pi f t)$ doesn't make mathematical sense. Your second equation is correct.

For parts b) and c), what does the wave motion consist of in terms of the motion of the string?

For part b & c, I am confused about how to compute, if you can help me I shall be thankful to you!

 

[Ammar2211]

Anybody can help me to solve part b & c, and directions please...

 

[PeroK]

Anybody can help me to solve part b & c, and directions please...

A wave on a string is created by each point of the string moving up and down in simple harmonic motion. You can see that by fixing $x = x_0$ and then looking at how the string at the point $x_0$ moves over time.

 

[Ammar2211]

A wave on a string is created by each part of the string moving up and down in simple harmonic motion. You can see that by fixing $x = x_0$ and then looking at how the string at the point $x_0$ moves over time.

So, how to find out max. velocity & max. acceleration!

 

[PeroK]

So, how to find out max. velocity & max. acceleration!

How are these defined?

 

[Ammar2211]

How are these defined?

A harmonic wave with a frequency of 80Hz and an amplitude of 0.025m travels along a string to the right with a speed of 12m/s.
a) Write a suitable wave function for this wave.
b) Find the maximum speed of a point on the string.
c) Find the maximum acceleration of a point on the string.

This is the problem statement, I don't know what's your point!

 

[PeroK]

A harmonic wave with a frequency of 80Hz and an amplitude of 0.025m travels along a string to the right with a speed of 12m/s.
a) Write a suitable wave function for this wave.
b) Find the maximum speed of a point on the string.
c) Find the maximum acceleration of a point on the string.

This is the problem statement, I don't know what's your point!

How are velocity and acceleration defined?

 

[Ammar2211]

How are velocity and acceleration defined?

I don't know, that's why I am asking here!

 

[PeroK]

I don't know, that's why I am asking here!

We can't teach you physics here, we can only help you with problems. To learn physics you need to be following a course or textbook or online lecture series or something of the sort. We would expect the source of your homwork question to have the material on which the question is based.

The subject matter here is harmonic waves and harmonic motion generally. If you really don't know what velocity and acceleration are, then you'll need to find some material on them. Without that you are not in a position to learn more advanced physics.

 

[collinsmark]

Velocity, $v$, is

$v = \mathrm{\frac{change \ in \ displacment}{change \ in \ time}}$

Another way to describe velocity is "rate of change of displacement."

Acceleration, $a$, is

$a = \mathrm{\frac{change \ in \ velocity}{change \ in \ time}}$

Another way to describe acceleration is "rate of change of velocity."

You already have the point's displacement, $y$ as a function of time, $t$. So, find the rates of change, and then determine what the maximums are.