Speed of progressive waves numerical

[lionel messi.]

1. Homework Statement :
progressive waves of frequency 300 hz are superimposed to produce a system of stationary waves in which adjacent nodes are 1.5m apart.calculate speed of progressive waves?


2. The attempt at a solution:
should i use
1)v=f*λ=300m/s
or
2)v=f*(2λ)=900m/s

 

[collinsmark]

1. Homework Statement :
progressive waves of frequency 300 hz are superimposed to produce a system of stationary waves in which adjacent nodes are 1.5m apart.calculate speed of progressive waves?2. The attempt at a solution:
should i use
1)v=f*λ=300m/s
or
2)v=f*(2λ)=900m/s

Be careful here.

The symbol for wavelength is pretty much always denoted as λ. And the velocity of a wave is always v = λf (where f is the frequency). This relationship wasn't used correctly in 2), given your choice of variable names.

(Not to mention that the math in 1 isn't right either; 300 x 1.5 ≠ 300)

What you should be asking yourself is "how many nodes occur in one wavelength?"

Try plotting cos x on a piece of paper. Don't forget to put the x-axis and y-axis on the plot. From one peak to the next peak of the function (one wavelength), how many times does the function cross the x-axis?

 

[lionel messi.]

sorry my bad @ 1.
in 2, I've used 2λ because the distance between 2 consecutive nodes is λ/2..so used L=λ/2 or 2L=λ which results in 900 m/s..

 

[collinsmark]

sorry my bad @ 1.
in 2, I've used 2λ because the distance between 2 consecutive nodes is λ/2..so used L=λ/2 or 2L=λ

That's good.

which results in 900 m/s..

Wait, you've determined a length. Just make sure you distinguish the difference between the wavelenth λ and the and the distance between nodes. Both are distances, but they are different distances.

Once you've determined λ, v = fλ still applies.