Let f be the frequency, v wav the speed, and T the period of a sinusoidal traveling wave. The correct relationship is:
a)f=1/T
b)f=vwav + T
c)f=vwavT
d)f=vwav/T
e)f=T/vwav
My thoughts:
Since frequency is equal to T=1/f so f=1/T. Vwav is connected to f by the equation v=lambda* frequency. so f=v/lambda. I have to connect the to f= equations inorder to get the relationship. I chose d because it seemed to combine the both.
For a transverse wave on a string the strong displacement is described as y(x,t)=f(x-at), where f is a given function and a is a positive constant. Which of the following does not necessarily follow this statement?
a)the shape of the string at time t=o is given by f(x)
b) the shape of the waveform does not change as it moves along a string
c) the waveform moves in the positive x direction
d) the speed of the waveform is a
e) the speed of the waveform is x/t
thoughts:
When I looked at the function equation y(x,t)=f(x-at). I thought to compare it with y(x,t)=f(kx-wt). I know that f can stand for Sin or Cos. I thought a can not be equal to the speed of the wave since v=w/k would equal it. So I chose d.
Thank you for your help.
For the first one, I believe the answer is a, as I learned in Honors Precalculus that frequency and period are indirectly related. That is, f=1/p and p=1/f. The equation is the same in a, though the variables are different. I could be wrong though.
correct, the other answers are silly. a is the correct answer.
but it says that you have to connect all three.v,f, and T. I thought of that to f=1/T.
Can you help me with the second?
I wish I could, but I haven't taken Physics. Sorry!
No problem! I can still help you understand how to approach the second question.
In the given equation y(x,t) = f(x - at), we have a wave described by the function f(x - at), where f is a given function and a is a positive constant.
Let's go through each option and see which one does not necessarily follow this statement:
a) The shape of the string at time t=0 is given by f(x).
This option is directly related to the statement. When t=0, the equation becomes y(x,0) = f(x - a * 0) = f(x), which matches option a. So this option does follow the statement.
b) The shape of the waveform does not change as it moves along a string.
In the given equation, the shape of the waveform is determined by the function f(x - at). As time progresses (t > 0), the argument of the function changes due to the factor of at. So the shape of the waveform does change as it moves along the string. Thus, option b does not necessarily follow the statement.
c) The waveform moves in the positive x direction.
In the given equation, we have the term (x - at), where a is a positive constant. This means that as time progresses (t > 0), the argument of the function decreases, causing the waveform to move in the positive x direction. So option c does necessarily follow the statement.
d) The speed of the waveform is a.
In the equation, the term (x - at) represents the distance traveled by the waveform in a given time period. The speed of the waveform is determined by the coefficient of t, which is -a. Therefore, the speed of the waveform is -a, not necessarily a. So option d does not necessarily follow the statement.
e) The speed of the waveform is x/t.
The speed of the waveform is determined by the coefficient of t in the equation (x - at). It is not directly proportional to x/t. So option e does not necessarily follow the statement.
Based on the above analysis, the correct answer is option d) The speed of the waveform is a.
I hope this explanation helps clarify the reasoning behind the correct answer. Let me know if you have any further questions!
No problem! I can still try to help you with the second question.
The correct answer is (e) the speed of the waveform is x/t.
In the given equation y(x,t) = f(x-at), the wave is described as moving in the positive x direction with a speed of 'a'. Since 'a' is a positive constant, it indicates the speed at which the wave travels along the string.
The equation does not indicate any relation between the speed of the waveform and the ratio of 'x' and 't', i.e., x/t. Therefore, statement (e) does not necessarily follow this equation.
The shape of the string at time t=0 being given by f(x) (a) follows from the equation.
The fact that the shape of the waveform does not change as it moves along a string (b), and the waveform moves in the positive x direction (c), both also follow from the given equation.
The statement that the speed of the waveform is 'a' (d) is also derived from the equation, since 'a' represents the speed at which the wave travels along the string.