How Do You Calculate Max and Min Transverse Speeds in a Wave on a String?

In summary, the given wave equation for particles on a string is D=0.40sin(7.0x+38t), where D is displacement in meters, x is position, and t is time in seconds. The wave speed is equal to 5.4 m/s. To find the maximum and minimum transverse speeds of the particles, you can differentiate the displacement equation with respect to time, giving you an equation for the speed of the particles. This can be solved for the maximum and minimum speeds.
  • #1
sadieboo24
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Homework Statement


You have a long string, and you oscillate one end, causing a (transverse) wave to propagate along it. The wave's formula is D=0.40sin(7.0x+38t) where displacement D and position x are given in meters and time t is given in seconds.

Determine the maximum and minimum transverse speeds of particles of the string.

Homework Equations


v= omega/k

The Attempt at a Solution


I found the wave speed, which is equal to 5.4 m/s, but I am not sure how to find the maximum and minimum speeds from this.
 
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  • #2
The given wave equation for the particles on the string is sinusoidal. Note that this equation is for the motion of the individual particles on the string, and so how would you obtain the equation describing the speed of the individual particles (from the displacement equation given to you)?

Hint: It's not v = ω/k
 

Related to How Do You Calculate Max and Min Transverse Speeds in a Wave on a String?

What is the equation for calculating wave speed on a string?

The equation for calculating wave speed on a string is 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.

How does tension affect wave speed on a string?

Tension and wave speed on a string are directly proportional. This means that as tension increases, wave speed also increases. This is because a higher tension allows the waves to travel faster through the string.

What is the relationship between linear density and wave speed?

Linear density and wave speed on a string are inversely proportional. This means that as linear density increases, wave speed decreases. This is because a higher linear density creates more resistance to the waves and slows them down.

Can wave speed on a string be greater than the speed of light?

No, wave speed on a string cannot exceed the speed of light. The speed of light is the fastest speed at which any form of energy can travel, and wave speed on a string is limited by the properties of the string itself.

How does the length of a string affect wave speed?

The length of a string has no direct effect on wave speed. However, a longer string may allow for more waves to exist and therefore increase the frequency of the waves, which in turn affects the wavelength and wave speed. Additionally, a longer string may have a different tension and linear density, which can also impact wave speed.

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