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:
I think the answer is D.Since frequency is equal to T=1/f so f=1/T. Vwav is connected to f by the equation v=lambda* frequency. so together you
so I figured that it would come out to be f=vwav/T
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:
I think the statement that does not necessarily apply is d. The a in the equation is not refering to the wave speed but to the angular frequency or w based on the equation.
y=Ysin(kx-wt)
I was told the problem answers were wrong. Could someone please help me on how to go about answering these problems correctly, so I can study how it is done.
For the first question, you are correct in identifying that frequency is equal to the reciprocal of the period (f = 1/T). However, the relationship between frequency, speed (vwav), and period (T) is given by the equation:
v = f * λ
where λ represents the wavelength. Therefore, we can rearrange the equation to solve for f:
f = v / λ
Since the wave speed (vwav) is equal to the wavelength (λ) divided by the period (T), we can substitute this into the equation:
f = (λ / T)
Thus, the correct relationship is e) f = T / vwav.
For the second question, the given equation y(x,t) = f(x - at) describes a traveling wave on a string where f is a given function and a is a positive constant. This equation represents a wave moving in the positive x-direction with a speed of a.
Now let's analyze the options:
a) The shape of the string at time t = 0 is given by f(x).
This statement is accurate because when t = 0, the equation simplifies to y(x, 0) = f(x), which describes the shape of the string at that particular moment.
b) The shape of the waveform does not change as it moves along a string.
This statement is also accurate because the equation y(x,t) = f(x - at) implies that the shape of the waveform is determined solely by the function f(x) and does not change as time progresses.
c) The waveform moves in the positive x-direction.
This statement is correct since the equation includes (x - at), indicating that the wave is traveling in the positive x-direction.
d) The speed of the waveform is a.
This statement is accurate because the constant a in the equation represents the speed at which the waveform is moving.
e) The speed of the waveform is x/t.
This statement is incorrect and does not necessarily follow the given equation. The wave speed is determined by the constant a, not by the variables x and t.
Therefore, the statement that does not necessarily follow the given equation is e) the speed of the waveform is x/t.