Finding the velocity of a standing wave

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Homework Help Overview

The problem involves calculating the velocity of a standing wave based on the distance between nodes and the frequency of the wave. The original poster provides specific measurements and attempts to apply relevant equations to find the solution.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between wavelength and the distance between nodes, with some suggesting that the distance between two nodes can be used to infer the wavelength. Questions arise about the correct interpretation of these measurements and the implications for calculating wave velocity.

Discussion Status

There is an ongoing exploration of the relationship between the measurements provided and the calculations needed. Some participants have offered guidance regarding unit conversions and the importance of using consistent measurement systems. The discussion reflects a mix of interpretations and attempts to clarify the problem without reaching a consensus.

Contextual Notes

Participants note the importance of using meters instead of centimeters for calculations, highlighting a common source of confusion in physics problems. The original poster acknowledges a mistake in unit conversion that may have affected their calculations.

JRibaudo2813
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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 wavelength, 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!
 
Last edited:
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Hello and welcome to PF!

JRibaudo2813 said:
[*]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?
 

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TSny said:
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.
 
Be careful of your units also.
 
JRibaudo2813 said:
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?
 

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Last edited:
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.
 
barryj said:
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!
 
barryj said:
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.
 

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