# Wave motion problems

1. Nov 25, 2005

### ilovephysics

first i have a quick question, for average power of a transverse harmonic wave the equation has the quantities tension, frequency and amplitude. the question asks me to find how much i need to change each quantity to increase the power by a factor of 100, i understand all that but then it asks me which quantity is the easiest to change. i got that the tension needed to be increased by a factor of 10000, and the frequency and amplitude only needed a factor of 10, im not quite sure if frequency or amplitude is easier to change, im guessing frequency because amplitude cannot be directly changed, whereas frequency you just move the string up and down faster?

anyways to the question im having trouble with:

1) the linear mass density of a nonuniform wire under constant tension decreases gradually along the wire so that an incident wave is transmitted without reflection. The wire in uniform for -infinity < x <= 0. In this region a transverse wave has the form y(x,t) = 0.003cos(25x-50t) with x,y in meteres and t in seconds. From x = 0 to x =20m the mass density decreases from initial mass density to (initial mass density / 4). For 20<= x < infinity, the mass density is constant at (initial mass density / 4). a) what is the wave velocity for large values of x b)what is the amplitude for large values of x? c) give y(x,t) for the large values of x

i got part a and it turns out to be 4 m/s, but i dont know what to do to get the amplitude, also in part c how do i find the k and w(omega)? is the k constant?

2. Nov 25, 2005

### mezarashi

To your first set of questions:

If your vibrating your guitar string and its amplitude is 1 cm right now. You're telling me you want to increase it to 10cm? Tension is out of the story. Originally we had to pull it by 100N, now we need to pull it by 100000N. I doubt any material would withstand that.

I'll come back to your second question later if nobody tackles it.

3. Nov 25, 2005

### ilovephysics

so which would be easier to change, amplitude of frequency? we both need to change them by a factor of 10

for the 2nd question im just not sure how to get the amplitude

4. Nov 25, 2005

### lightgrav

Q#2:

Get the amplitude for the wave on the thick (negative x) side.

Is the speed the same? wave count/second or wave count/meter ?

No reflection ...
which do you suppose is the same for negative and positive x :
Energy /second, E/meter, E/wave; or momentum/sec ...
or transverse (restoring) Force (maximum) ; or is it acceleration?

Last edited: Nov 25, 2005