Some specific questions about waves

[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.

 

[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

 

[Andrew Mason]

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.

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

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.

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?

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.

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

AM