Physics Study Guide/Standing waves

Physics Study Guide (Print Version)
Units Linear Motion Force Momentum Normal Force and Friction Work Energy
Torque & Circular Motion Fluids Fields Gravity Waves Wave overtones Standing Waves Sound
Thermodynamics Electricity Magnetism Optics
Physical Constants Frictional Coefficients Greek Alphabet Logarithms Vectors and Scalars Other Topics

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.


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.