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.

 

[Nickie]

The correct equation to use for calculating the speed of progressive waves is v = f * λ, where v is the speed of the wave, f is the frequency, and λ is the wavelength. In this case, the frequency is given as 300 Hz and the distance between adjacent nodes (which is equal to half the wavelength) is 1.5m. Therefore, the wavelength is 2 * 1.5m = 3m. Plugging in these values, we get v = 300 Hz * 3m = 900m/s. Therefore, the speed of the progressive waves in this system is 900m/s.