What is a wave constant and how do you find the phase of a wave?

[yjk91]

Homework Statement

y = (0.10 m)sin(0.77x − 37t),
where x and y are in meters and t is in seconds. If the linear mass density of the string is 11 g/m, determine the following.

the phase constant is 0 rad, but I'm not sure why and what phase constant exactly is couldn't' find it in the book. can anybody explain it to me?


the phase of the wave at x = 4 cm and t = 0.1 s

so i just plugged it into the equation but that does not seem to be the case..

i'm lost.. and the book doesn't have anything about these

help and thank you

 

[JesseC]

So it looks like your wave is of the form:

$$y = A \sin (kx-\omega t)$$

thus it seems to me that y is the amplitude of the wave at a given time and distance along the string. It looks like you've confused amplitude (height) with phase! Just plugging in values for x and t into that equation will give you the amplitude.

In the case of plane waves such as yours, the phase is an arbitrary constant related to where you choose to put the zero of your axes. So really it doesn't make sense to ask what is the phase at a particular point or time because it is a constant. But you are right, for the wave given the phase has been set to zero. If it wasn't set to zero your wave may look like this:

$$y = A \sin (kx-\omega t + C)$$

where C is the arbitrary phase constant.

 

[yjk91]

So it looks like your wave is of the form:

$$y = A \sin (kx-\omega t)$$



In the case of plane waves such as yours, the phase is an arbitrary constant related to where you choose to put the zero of your axes. So really it doesn't make sense to ask what is the phase at a particular point or time because it is a constant. But you are right, for the wave given the phase has been set to zero. If it wasn't set to zero your wave may look like this:

$$y = A \sin (kx-\omega t + C)$$




where C is the arbitrary phase constant.

this is an example

A sinusoidal wave on a string is described by the equation y = (0.10 m)sin(0.73x − 42t),
where x and y are in meters and t is in seconds. If the linear mass density of the string is 11 g/m, determine the following.


the phase of the wave at x = 1 cm and t = 0.1 s

answer = -4.19 rad

this one has an answer but I'm not sure how to solve it

 

[JesseC]

You've calculated 0.73x − 42t at x = 1 cm and t = 0.1 s to be equal to -4.19 right? That is not the same thing as the phase... that's just the argument of the sine function at a particular point in time and space. The phase of a wave remains constant relative to some arbitrary reference point.

Perhaps you should post the entire question you have a problem with and we could see what is actually going on here...

 

[yjk91]

You've calculated 0.73x − 42t at x = 1 cm and t = 0.1 s to be equal to -4.19 right? That is not the same thing as the phase... that's just the argument of the sine function at a particular point in time and space. The phase of a wave remains constant relative to some arbitrary reference point.

Perhaps you should post the entire question you have a problem with and we could see what is actually going on here...

A sinusoidal wave on a string is described by the equation
y = (0.10 m)sin(0.73x − 42t),
where x and y are in meters and t is in seconds. If the linear mass density of the string is 11 g/m, determine the following.
(a) the phase constant
A: 0 rad

(b) the phase of the wave at x = 1 cm and t = 0.1 s
A: -4.19 rad
these the questions and answers

thank you

 

[JesseC]

So its clear now I was using phase constant and phase interchangeably whereas the question doesn't in which case it seems like your answers are correct.

 

[yjk91]

-4.19 rad
how do get to this answer is my question you find 2 equations with unkwon amplitude
and divide them but i got 30 degree as my angle but is this right?

 

[vela]

Check your units.