How Do You Calculate the Wavelength of Colliding Waves?

[ixerr]

Homework Statement

Two sinusoidal waves with equal wavelengths travel along a string in opposite directions at 7.72 m/s. The time between two successive instants when the antinodes are at a maximum height is 0.324 s. What is the wavelength (in m)?

Homework Equations

vt=x
Also,
Propagation speed = wavelength * frequency = wavelength / period time

The Attempt at a Solution

I tried many, many different ways to solve this equation but ultimately I keep getting the wrong answer.. Here is one of the attempts:
The distance between two successive antinodes or two successive nodes is equal to the wavelength of the wave. I figured out the distance based on the speed of the wave and the time between two antinodes with vt = x (since there is no acceleration).
(7.72)(0.324)= 2.50128 m
Yet it is not the right answer? Can anyone give me any more insight on what I can do..?

 

[BruceW]

The question is a bit vague... does it mean both waves are moving at 7.72 m/s in opposite directions? so their relative velocity is 15.44 m/s ? And it seems to suggest standing waves, but it doesn't mention the end points of the string, so really the two waves could have any phase difference.

If I was guessing, I'd say each of the waves is moving at 7.72 m/s so their relative velocity is 15.44 m/s and I'd guess the situation is standing waves caused by the string being fixed at one end. But what do you think? was there more information?

 

[ixerr]

Yes! :) I got the answer, the velocity was 15.44 m/s. Thanks!

 

[BruceW]

alright, cool

 

[asteriatic]

I can provide a response to your question about the wavelength. The wavelength is defined as the distance between two successive points on a wave that are in phase, meaning they have the same amplitude and traveling in the same direction. In this case, we are dealing with two sinusoidal waves traveling in opposite directions on a string. The distance between two successive antinodes or nodes on these waves would be equal to the wavelength.

To solve this problem, we can use the equation for propagation speed, which is equal to the wavelength multiplied by the frequency. In this case, we are given the propagation speed (7.72 m/s) and the period time (0.324 s). We can use the equation to find the frequency, which is equal to 1/period time. Therefore, the frequency would be 1/0.324 = 3.086 Hz.

Now, we can use the equation for propagation speed to calculate the wavelength. Plugging in the values, we get:
7.72 m/s = wavelength * 3.086 Hz
Wavelength = 7.72 m/s / 3.086 Hz = 2.501 m

Therefore, the wavelength of these two sinusoidal waves on the string is 2.501 m. I hope this helps to clarify the concept of wavelength and how to solve this problem. Let me know if you have any further questions.