Wave speed of a stretched string

In summary, wave speed is dependent on the properties of the medium, such as its elasticity and mass. The frequency of the wave depends on the source of the wave, while the wavelength is determined by the relation v = λƒ. The source of the wave may also play a role in wave speed through dispersion, but this is not the main factor. Overall, the medium has a significant impact on the speed of the wave, and different combinations of frequency and wavelength can result in the same speed.
  • #1
duran9987
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A bit confused here as to what wave speed is dependent on. At first I learned that v = λƒ, and a couple of pages later in my textbook I find that v = √(τ/μ). Also, I found that speed is only dependent on the properties of the medium, specifically its elasticity and mass. Where does wavelength and frequency come into play if the medium is the only dependent?
 
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  • #2
The frequency of the wave depends on the source of the wave (how it is being generated). If you consider a wave on a rope, how frequently you wave your arm up and down will determine the frequency of the wave.
The speed of the wave depends on the tension in and density of the rope. So the medium determines the speed of the wave, but there are infinite combinations of frequency and wavelength that will give the correct speed.
For a given rope under a given tension, the wave will travel at a certain speed and the wavelength will depend on the frequency according to [itex]\lambda=\frac{v}{ƒ}[/itex].
 
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  • #3
The medium plays a very big role in wave speed. If the waves travel along a string, the lower the mass and greater the density of the string, the faster waves travel across the string. Waves also travel much more slowly in the air than they do underwater or along a dense string. I'm sure the source of the wave plays a role in its speed as well, but I'm not sure how. This source has some information on it: http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_WavesAlongStrings.xml
 
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  • #4
Zachary Samples said:
The medium plays a very big role in wave speed. If the waves travel along a string, the lower the mass and greater the density of the string, the faster waves travel across the string. Waves also travel much more slowly in the air than they do underwater or along a dense string. I'm sure the source of the wave plays a role in its speed as well, but I'm not sure how. This source has some information on it: http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_WavesAlongStrings.xml
The source does not play any role in wave speed other than through the fact that some media have dispersion relations such that the wave velocity is frequency dependent. The relation v = λf can rather be thought of as relating the frequency and wave length for a given wave velocity, i.e., for a wave with wave velocity v, a wave of frequency f will have wave length λ = v/f. Of course, if you measure the wave length and frequency, you can infer what the velocity is (and thus obtain information on the internal properties of the medium).
 
  • #5


The wave speed of a stretched string is dependent on both the properties of the medium and the wavelength and frequency of the wave. The equation v = λƒ represents the relationship between wave speed, wavelength, and frequency in a general sense. However, in the specific case of a stretched string, the equation v = √(τ/μ) takes into account the tension (τ) and linear mass density (μ) of the string, which are properties of the medium. Therefore, the wave speed of a stretched string is determined by a combination of both the properties of the medium and the wavelength and frequency of the wave. It is important to consider all factors when studying the behavior of waves in different mediums.
 

FAQ: Wave speed of a stretched string

1. What is the wave speed of a stretched string?

The wave speed of a stretched string is the speed at which a wave travels through the string. It is dependent on the tension and density of the string, as well as the wavelength and frequency of the wave.

2. How is the wave speed of a stretched string calculated?

The wave speed of a stretched string can be calculated using the formula v = √(T/μ), where v is the wave speed, T is the tension in the string, and μ is the linear density of the string.

3. Does the wave speed of a stretched string change if the tension or density is altered?

Yes, the wave speed of a stretched string is directly proportional to the tension and inversely proportional to the density. This means that increasing the tension or decreasing the density will result in a higher wave speed, and vice versa.

4. Can the wave speed of a stretched string be greater than the speed of light?

No, the wave speed of a stretched string is limited by the properties of the string itself and cannot exceed the speed of light. In fact, the wave speed in a string is usually much slower than the speed of light, typically ranging from a few meters per second to a few hundred meters per second.

5. How does the wave speed of a stretched string affect the pitch of a sound produced by the string?

The wave speed of a stretched string affects the pitch of a sound produced by the string because it determines the frequency of the wave. A higher wave speed results in a higher frequency, which corresponds to a higher pitch. This is why tightening the strings on a musical instrument can increase the pitch of the sound produced.

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