# What units for the wave function of a string?

• Zouatine
The function Ψ(x,t) describes the displacement of a wave in terms of position and time. The unit of φ(x) is length and the unit of sin(ωt+α) is dimensionless.
Zouatine
Homework Statement
unit of wave function
Relevant Equations
Ψ(x,t)=φ(x)*sin(ωt+α)
hello , hope all of you are doing well ,

i have question about the unit of the function of waves of string fixed in both boundary , the function of waves is function of two variables x and t , so it's function describe the displacement in function of place and time ,
Ψ(x,t)=φ(x)*sin(ωt+α)
φ(x): is the shape function
ω= 2πν : the angular frequency ν: is the frequency, Hz
α : initial phase

I'm confusing about the unit of this function , i think the unit must be unit of length ( cm , mm ... ) because from the definition we said it's function describe the displacement , and second think is : sin(ωt+α) doesn't have unit and φ(x) must be unit of length . am i right ?

thank you

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## 1. What is the unit of measurement for the wave function of a string?

The unit of measurement for the wave function of a string is typically meters (m) or centimeters (cm), as it represents the displacement of the string from its equilibrium position.

## 2. Can the wave function of a string be measured in other units?

Yes, the wave function of a string can also be measured in other units such as millimeters (mm) or inches (in), depending on the scale of the string and the precision of the measurement.

## 3. How is the wave function of a string related to frequency?

The wave function of a string is directly proportional to the frequency of the wave traveling through the string. This means that as the frequency increases, the amplitude of the wave function also increases.

## 4. Is the unit of the wave function of a string the same as the unit for wavelength?

No, the unit for wavelength is typically meters (m) or centimeters (cm), while the unit for the wave function of a string is also meters (m) or centimeters (cm) but represents a different physical quantity.

## 5. Can the unit of the wave function of a string change?

Yes, the unit of the wave function of a string can change depending on the scale of the string and the precision of the measurement. It is important to use consistent units when working with the wave function of a string to avoid confusion and errors.

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