Travelling wave: finding the velocity from displacement

[kamhogo]

Hi everyone. I have trouble finding the velocity of a traveling wave give some information about it's displacement. I am given D (x,t)= 1 cm if |x - 4t| <\= 1 &&&D (x,t) = 0 cm if |x - 4t| > 1. I don't know how to interpret these mathematical statements. I've been trying for 3 hours now :(. I have the feeling that it's simple but I simply don't get it. 1) Do they mean that the wave number k=1 and the angular frequency omega=4? ( Inferred from the formula D (x,t)= A cos ( kx +/- wt + phase constant). Does it also mean that the phase constant =0 rad? 2) Am I able to draw a snapshot or hiatory graph from these statements only? If so, can someone give me a hint as of how to proceed? 3) I am asked to find the velocity of the wave. Hint as of how to do that please? Thanks in advance for any help!

 

[kamhogo]

Hi everyone. I have trouble finding the velocity of a traveling wave give some information about it's displacement. I am given D (x,t)= 1 cm if |x - 4t| <\= 1 &&&D (x,t) = 0 cm if |x - 4t| > 1. I don't know how to interpret these mathematical statements. I've been trying for 3 hours now :(. I have the feeling that it's simple but I simply don't get it. 1) Do they mean that the wave number k=1 and the angular frequency omega=4? ( Inferred from the formula D (x,t)= A cos ( kx +/- wt + phase constant). Does it also mean that the phase constant =0 rad? 2) Am I able to draw a snapshot or hiatory graph from these statements only? If so, can someone give me a hint as of how to proceed? 3) I am asked to find the velocity of the wave. Hint as of how to do that please? Thanks in advance for any help!

Sorry for the typos!

 

[nasu]

This is not a sine wave but a pulse. You cannot identify k and omega. But you don't need to.
You can draw the wave at t=0 (for example) and then at some other value of t. 1 second, maybe.
This will show you how the wave front travels.

 

[kamhogo]

This is not a sine wave but a pulse. You cannot identify k and omega. But you don't need to.
You can draw the wave at t=0 (for example) and then at some other value of t. 1 second, maybe.
This will show you how the wave front travels.

Thank you! I drew the wave at t=0s and and at t=1s and found the the displacement over one second (velocity)!