Given the frequency and wavespeed, find k

[JoeyBob]

Homework Statement

See attachment

Relevant Equations

y(x, t) = Asin(kx-wt+2pi)

First I tried looking at the units of the answer, 1/m. Frequency is also 1/s and since I also have m/s, if i divide the frequency by the wave speed I get 1/m (same units as the answer). This gave the wrong answer though.

Next I tried looking at the equation at t=0. y(x)=Asin(kx+2pi). I can then get k=-2pi/x, but I need another equation to find x. I decided to try and take the derivative of y(x) to get Axcos(kx+2pi) = -331 <-- wave velocity

The issue not though is that idk how to isolate x on this equation since its both inside cos and outside. If I take arccos of both sides it doesn't help because i get

Arccos(Axcos(kx+2pi) = arccos(-331)

Im stuck at this point. Btw the answer is supposed to be -11.75

 

[haruspex]

Asin(kx-wt+2pi)? Why the +2pi? Doesn't change anything.

if i divide the frequency by the wave speed I get 1/m (same units as the answer). This gave the wrong answer though.

What numbers are you given and what answer did you get?

take the derivative of y(x) to get Axcos(kx+2pi) = -331 <-- wave velocity

No, that gives the rate of change of y at a given (x,t). Wave speed is how fast the wave appears to move in the x direction, i.e. how fast a local max or min shifts along.

 

[JoeyBob]

What numbers are you given and what answer did you get?

so f=619Hz, speed of sound (in this question) = 331 m/s.

619 Hz/331m/s = 1.87 (1/m)

Asin(kx-wt+2pi)? Why the +2pi? Doesn't change anything.

Youre right I guess but then at the same time it does nothing bad.

 

[haruspex]

f=619Hz

What is the relationship between that and ω?

Think about this: you want the speed at which the profile of the wave moves. That is, as a short time δt goes by, each given value of y is to be found at δx further along in the direction of travel. So your task is to find what combination of δx and δt leads to the same observed y.

 

[JoeyBob]

What is the relationship between that and ω?

Think about this: you want the speed at which the profile of the wave moves. That is, as a short time δt goes by, each given value of y is to be found at δx further along in the direction of travel. So your task is to find what combination of δx and δt leads to the same observed y.

So there's some sort of equation that relates k and f that I have to derive somehow?

 

[haruspex]

So there's some sort of equation that relates k and f that I have to derive somehow?

No, there's an equation relating k and f to the speed of the wave. You were close, but off by a constant factor. You can figure it out by the means I outlined in post #4.
Given y at some position x and time t is Asin(kx-wt), what is the change in y if you go δx to the right? What is the change in y if you look again at time δt later? What combination of these two changes would leave y unchanged?

 

[JoeyBob]

No, there's an equation relating k and f to the speed of the wave. You were close, but off by a constant factor. You can figure it out by the means I outlined in post #4.
Given y at some position x and time t is Asin(kx-wt), what is the change in y if you go δx to the right? What is the change in y if you look again at time δt later? What combination of these two changes would leave y unchanged?

I don't think I fully understand. δx would be kAcos(kx-wt) and δt would be -wAcos(kx-wt). But combining them would not leave y unchanged unless k=w. I just calculated w from the frequency and its 3889, which is not the answer.

 

[haruspex]

δx would be kAcos(kx-wt) and δt would be -wAcos(kx-wt)

You've left out the factors δx and δt.