# Some specific questions about waves

1. Jun 1, 2005

### PinkSheep

Okay, I have this study guide for a test, but I'm having troubles figuring out the answers...so these are some things I'm wondering:

1. If you have a taut string, by what factor would you have to increase the tension to double the wave speed?
I think it's 4, but I'm not sure.

2. If a string is under constant tension and generates a harmonic wave, by what factor would the amplitude and speed change if the power is doubled?
I have no clue on this one.

3. And how would you go about solving this problem: A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40 vibrations in 30s. A given peak travels 5m along the rope in 2s. What is the wavelength?
I know wavelength equals speed divided by frequency...but I don't know what to use as speed or frequency, so therein lies my problem.

Any help and/or explanations would be greatly appreciated.

2. Jun 2, 2005

### Pyrrhus

Why don't you try it at the equation so you will be sure?

$$v = \sqrt{\frac{T}{\lambda_{density}}$$

Example

$$v = \sqrt{\frac{4T}{\lambda_{density}}$$

$$v = 2 \sqrt{\frac{T}{\lambda_{density}}$$

$$v_{new} = 2 v_{old}$$

What is the definition of frequency????

frequency = oscilations/time

Last edited: Jun 2, 2005
3. Jun 2, 2005

### Andrew Mason

Use:
$$v = \sqrt{\frac{T}{m/L}}$$

The energy of a mass, dm, undergoing simple harmonic motion, is proportional to the square of its amplitude. This is apparent, for example, in a mass spring system where the energy of the mass is $\frac{1}{2}kx^2$.
The power is the time rate of change of energy. So how is the power related to the speed and the square of the amplitude?

The speed is 2.5 m/sec. The frequency is 80 cps. Solve for wavelength.

AM