Sinusoidal Wave: Double Frequency, Double Speed

In summary, a sinusoidal wave with double frequency and double speed is a wave that has a higher frequency and travels at a faster speed compared to a regular sinusoidal wave. The frequency of the wave is directly proportional to its speed, and this relationship is described by the equation v = fλ. This type of wave has various applications in telecommunications, medical imaging, and music and sound production. The amplitude of the wave is not affected by its frequency and speed, but it may appear to decrease due to the shorter duration of each cycle. A sinusoidal wave with double frequency and double speed can be graphically represented by a wave with a higher frequency and shorter wavelength, a steeper slope, and a doubled number of cycles within a given time
  • #1
Andy_ToK
43
0

Homework Statement


A sinusodial wave is moving along a string of uniform density. If you double the frequency of the wave,

a)the speed of the wave doubles
b)the speed of the wave remains about the same


Homework Equations


v=lambda*f


The Attempt at a Solution


I chose a) using the equation v=lambda*f. as f doubles, v doubles too.
 
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  • #2
That would only be true if the wavelength remained the same.

What determines the speed of a wave on a string?
 
  • #3
tension and density.

The answer is b)
 

1. What is a sinusoidal wave with double frequency and double speed?

A sinusoidal wave with double frequency and double speed is a type of wave that has a higher frequency and travels at a faster speed compared to a regular sinusoidal wave. This means that the wave completes two cycles in the same amount of time it takes for a regular sinusoidal wave to complete one cycle.

2. How is the frequency of a sinusoidal wave related to its speed?

The frequency of a sinusoidal wave is directly proportional to its speed. This means that as the frequency doubles, the speed of the wave also doubles. This relationship is described by the equation v = fλ, where v is the speed, f is the frequency, and λ is the wavelength.

3. What are the applications of a sinusoidal wave with double frequency and double speed?

A sinusoidal wave with double frequency and double speed has various applications in different fields. It is commonly used in telecommunications, such as in high-speed internet connections and satellite communications. It is also used in medical imaging, such as in MRI scans, and in music and sound production, such as in high-quality audio systems.

4. How is the amplitude of a sinusoidal wave affected by its frequency and speed?

The amplitude of a sinusoidal wave is not affected by its frequency and speed. The amplitude is a measure of the wave's maximum displacement from its resting position and is only influenced by the energy of the wave. However, as the frequency and speed of the wave increase, the amplitude may appear to decrease due to the shorter duration of each cycle.

5. How can a sinusoidal wave with double frequency and double speed be graphically represented?

A sinusoidal wave with double frequency and double speed can be represented graphically by a wave with a higher frequency and shorter wavelength compared to a regular sinusoidal wave. It will also have a steeper slope on the graph, indicating a faster speed. Additionally, the amplitude of the wave will remain the same, but the number of cycles within a given time period will be doubled.

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