Finding the velocity of a standing wave

[JRibaudo2813]

1. The problem The distance between two consecutive nodes
of a standing wave is 21.9 cm. The hand generating the pulses moves up and down through
a complete cycle 3.72 times every 4.22 s.
Find the velocity of the wave.
Answer in units of m/s
2. Some relevant things to know are:

• Frequency equals the number of vibrations a wave makes per second
• to measure the wavelength of a wave, you must have the length between either: A) two antinodes (peaks,trofts,crests,etc.) or B) THREE nodes. Since we only know the length between two nodes, it is assumed that we can multiply the distance (21.9 cm) by 1.5 to figure out the distance between three nodes.
• and finally, once you determine both the frequency and the wavelenght, you must know how to deduce the velocity out of both. the equation for that is v=fλ

3. Attempts I have attempted this problem several times using the above equations and methods. I came upon the answer 28.9578199052 m/s (≈29m/s) but apparently that is wrong.Thank you for any help you can provide, cheers!

Edit: my sincere apologies for butchering the template, sorry, I'm new here!

 

[TSny]

Hello and welcome to PF!

[*]to measure the wavelength of a wave, you must have the length between either: A) two antinodes (peaks,trofts,crests,etc.) or B) THREE nodes. Since we only know the length between two nodes, it is assumed that we can multiply the distance (21.9 cm) by 1.5 to figure out the distance between three nodes.

How is the wavelength related to the distance between two consecutive nodes?

 

[JRibaudo2813]

Hello and welcome to PF!



How is the wavelength related to the distance between two consecutive nodes?

My physics teacher taught us that you can measure wavelength by finding the lambda values. So we count 1λ, 1.5λ, 2λ. etc. etc. Then we use the equation (#λ)(λ)=length of wave segment. Three nodes would be one lambda value and two antinodes would be one lambda segment.

 

[barryj]

Be careful of your units also.

 

[TSny]

My physics teacher taught us that you can measure wavelength by finding the lambda values. So we count 1λ, 1.5λ, 2λ. etc. etc. Then we use the equation (#λ)(λ)=length of wave segment. Three nodes would be one lambda value and two antinodes would be one lambda segment.

What is the distance in cm between nodes N₁ and N₂? Between N₁ and N₃? What is the wavelength in cm?

 

[barryj]

In physics, to be safe, use meters not cm. There are many constants in physics that assume you are using mks units, i.e. meters, kilograms, and seconds. Recall in chemistry you might use cgs units, centimeters, grams, and seconds.

 

[JRibaudo2813]

Be careful of your units also.

Ah yes, this is probably the one thing I always over looked, units!

Thank you, I'm going to try it again later!

 

[JRibaudo2813]

In physics, to be safe, use meters not cm. There are many constants in physics that assume you are using mks units, i.e. meters, kilograms, and seconds. Recall in chemistry you might use cgs units, centimeters, grams, and seconds.

Yah, I just realized that my main issue was mixing up centimeters with meters. I found the velocity as cm/s but overlooked it and entered it as m/s.