(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A wave travels along a string in the positive x-direction at 30 m/s. The frequency of the wave is 50 Hz. At x = 0 and t = 0, the wave velocity is 2.5 m/s and the vertical displacement is y = 4 mm. Write the function y(x,t) for the wave.

2. Relevant equations

velocity = (wavelength)(frequency) = (angular velocity)/(wave number)

angular velocity = 2*pi*frequency

What the function should look like:

y(x,t) = Asin(kx - wt + θ)

A = amplitude

k = wave number

w = angular velocity

t = time (s)

θ = initial phase shift

3. The attempt at a solution

Figuring out the wave number (k) as well as the wavelength and angular velocity was the easy part:

w = 2*pi*(50 Hz) = 100*pi

wavelength = velocity/frequency = (30 m/s)/(50 Hz) = .6 m

wave number (k) = w/v = (100*pi)/(30 m/s) = 10.47 m^-1

So far the function looks like:

y(x,t) = Asin(10.47(x) - 314.16(t) + θ)

The only variables left to find are the amplitude (A) and initial phase shift (θ). I tried plugging in the initial conditions the problem gave me, but I end up with:

y(x,t) = Asin(θ) = .004

differentiating the function y(x,t) = Asin(10.47(x) - 314.16(t) + θ) with respect to time gives the velocity equation, which is:

v(x,t) = -A(314.16)cos(10.47(x) - 314.16(t) + θ)

and plugging in the initial conditions for velocity gives:

-A(314.16)cos(θ) = 2.5

I don't know where to go from here to find amplitude and the initial phase shift. I have tried setting the velocity equation equal to zero which would give me a critical point (amplitude), but that didn't help much. I've also tried using a substitution method between these two equations:

y(x,t) = Asin(θ) = .004

-A(314.16)cos(θ) = 2.5

but that didn't get me anywhere either. Any help would be greatly appreciated!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculating functions for wave problems

**Physics Forums | Science Articles, Homework Help, Discussion**