To calculate the wavelength of a transverse wave on a spring when you have the length of the spring and the frequency, you can use the formula:
wavelength = velocity / frequency
In this case, the velocity represents the speed of the wave propagation along the spring. For a wave traveling along a stretched spring, the velocity is determined by the tension in the spring and the mass per unit length of the spring.
If you know the tension in the spring and the mass per unit length, you can calculate the velocity using the formula:
velocity = sqrt(tension / mass per unit length)
Once you have the velocity and the frequency, you can substitute these values into the wavelength formula to find the wavelength.
It's important to note that this calculation assumes that the wave on the spring is a simple transverse wave and that the properties of the spring, such as its stiffness and mass per unit length, are uniform along its entire length.