Standing waves

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    Standing waves

    Wave speed is equal to the square root of tension divided by the linear density of the string.


    μ = m/L

    Linear density of the string is equal to the mass divided by the length of the string.


    λmax = 2L

    The fundamental wavelength is equal to two times the length of the string.

    Variables


    λ: wavelength (m)
    λmax: fundamental wavelength (m)
    μ: linear density (g/m)
    v: wave speed (m/s)
    F: force (N)
    m: mass (kg)
    L: length of the string (m)
    l: meters (m)

    Definition of terms

    Tension (F): (not frequency) in the string (t is used for time in these equations). Units: newtons (N)

    Linear density (μ): of the string, Greek mu. Units: grams per meter (g/m)

    Velocity (v) of the wave (m/s)

    Mass (m): Units: grams (g). (We would use kilograms but they are too big for most strings).

    Length of the string (L): Units: meters (m)

    Fundamental frequency: the frequency when the wavelength is the longest allowed, this gives us the lowest sound that we can get from the system.

    In a string, the length of the string is half of the largest wavelength that can create a standing wave, called its fundamental wavelength.