[Assume ideal conditions and simple harmonic wave]
My book showed resemblance in a lot of equations related to both transverse and longitudinal waves although they work very differently.
the displacement of particle's equation in a transverse wave can be:
$y=A\sin(\omega t-kx)$ where A is the amplitude.
while the displacement equation in a sound/longitudinal wave can be taken as:
$s=s_0\sin(\omega t-kx)$ where $s_o$ is the amplitude
Looking at these, I obviously concluded that just like the amplitude of all the particles in a transverse wave is A, the amplitude of the vibrations of all the particles in a sound wave must be equal as well with the value being, $s_0$
But in one of the problems, I found that this is not true. Why is it so? Is my book wrong about this or is there some error in my interpretation and understanding?
For reference, here is the problem(It was a matrix match type problem, so I'm just going to mention this specific problem and not the other parts):
Amplitude of vibration of all particles are equal in which of the following types of waves?
The options given were:
- Stationary waves
- Plane simple harmonic transverse waves
- Sound waves
- Standing waves in an open organ pipe
- Plane simple harmonic longitudinal waves
The answer given was:
2, 5 I understand how it is 2 and 5 but why is it not 3(that is, sound waves)