If a cannonball and a BB have the same speed, which has the longer wavelength?
The "de Brogle wavelength" of mass, when considered a quantum mechanical wave is
lambda = h/(mv)
where h is Planck's constant.
Of the two objects, the BB will have less momentum (mv) at a given velocity v, and therefore will have a longer wavelength
To determine which object has a longer wavelength, we first need to understand the concept of wavelength.
Wavelength is a measurement of the distance between two consecutive points of a wave, typically measured from peak to peak or trough to trough. In the context of objects in motion, wavelength is related to the concept of momentum.
The momentum of an object is given by the equation: momentum = mass × velocity.
In terms of wavelengths, the momentum of an object can also be expressed as: wavelength = Planck's constant / momentum.
Now, let's consider the two objects: a cannonball and a BB.
The question states that both objects have the same speed, which means they have the same velocity. Recall that velocity is a vector quantity that describes the rate at which an object changes its position. In this case, since both objects have the same speed, they are traveling at the same rate.
However, the cannonball and the BB differ in terms of their mass. A cannonball typically has a much larger mass compared to a BB, which means it has more inertia. The BB, on the other hand, has a smaller mass and less inertia.
Using the equation for momentum, we see that since the speed of both objects is the same, the cannonball will have a higher momentum due to its larger mass. Conversely, the BB will have a lower momentum due to its smaller mass.
Now, let's look at the equation for wavelength. Since the speed (or velocity) is the same for both objects, and the Planck's constant is a constant value, we can conclude that the object with higher momentum (greater mass) will have a shorter wavelength, while the object with lower momentum (smaller mass) will have a longer wavelength.
Therefore, in this scenario, the BB, which has a smaller mass and lower momentum, will have a longer wavelength compared to the cannonball.