# Resonance in standing waves

• twiztidmxcn
In summary, the conversation discusses the problem of resonance in standing waves in a long pipe that is closed on one end and open on the other. The goal is to find the frequency using the speed of sound in air. The speaker initially guesses the harmonic number to be 5, but is advised to use the fundamental frequency instead. The frequency is then calculated to be 148.28Hz using the equation L = (2n-1)*wavelength / 4 and the given length of the pipe. The conversation also clarifies the concept of fundamental frequency and how it relates to the length of the pipe.

#### twiztidmxcn

so my problem deals with resonance in standing waves

if you have a standing wave in a long pipe of length 2.90m and that is closed on the left end and open on the right end and the graph of it is as below, with x-axis the position along pipe and y-axis vertical air displacement

http://i2.photobucket.com/albums/y7/twiztidmxcn/plot.gif

i found the harmonic number to be 5, but that was by guessing at a wavelength

i now need to find frequency using the speed of sound in air as 344m/s

i used the harmonic number and the equation L = (2n-1)*wavelength / 4, pluggin in my length of 2.9m and 5 for n, and then divide 344 by that number

i have gotten a multitude of numbers, including 266.86Hz, but nothing has worked

any help in the right direction would be much appreciated

thx-twiztidmxcn

Are you trying to find the fundamental frequency? If so, then picking a harmonic number of 5 is no good, since this is not the fundamental. Use the most simple waveform you have, instead of that mutant fish thing, and you should have a more sensible answer.

it just says 'find the pitch (frequency) of the wave using 344m/s as the speed of sound in air'

i haven;t been taught any other kind of equations to use with this. my wavelength is inaccurately guessed and found to be close to right, I am fairly confused

twiztidmxcn said:
it just says 'find the pitch (frequency) of the wave using 344m/s as the speed of sound in air'

i haven;t been taught any other kind of equations to use with this. my wavelength is inaccurately guessed and found to be close to right, I am fairly confused

It looks to me like you're on the right track. From your graph it looks like the wavelength is between 2 and 2.5 (one full sinewave).

This corresponds to n = 3. Using your equation I get the wavelength = 2.32m
f=344/2.32 = 148.28Hz

I still don't understand why you've chosen a harmonic as the wave, rather than the fundamental.

The frequency that the pipe will resonate at is the fundamental frequency, which happens with the most simple wave, with the largest possible wavelength. At one end of the tube you have a node, the other end; an antinode.

brewnog said:
I still don't understand why you've chosen a harmonic as the wave, rather than the fundamental.

The frequency that the pipe will resonate at is the fundamental frequency, which happens with the most simple wave, with the largest possible wavelength. At one end of the tube you have a node, the other end; an antinode.

But look at the graph. It is not resonating at the "fundamental" frequency. The wavelength is less than the length of the tube.

learningphysics said:
But look at the graph. It is not resonating at the "fundamental" frequency. The wavelength is less than the length of the tube.

But the OP said that he'd guessed that.

learningphysics said:
It looks to me like you're on the right track. From your graph it looks like the wavelength is between 2 and 2.5 (one full sinewave).

This corresponds to n = 3. Using your equation I get the wavelength = 2.32m
f=344/2.32 = 148.28Hz

my friend, i thank you. this made sense, and i worked around with it and finally got how it worked out.

thank you.

## 1. What is resonance in standing waves?

Resonance in standing waves is a phenomenon that occurs when a standing wave (a wave that appears to be standing still) is created by two waves with the same frequency and amplitude traveling in opposite directions. This results in the reinforcement and amplification of the wave, causing it to have a larger amplitude.

## 2. How is resonance in standing waves related to frequency?

Resonance in standing waves is directly related to frequency. In order for resonance to occur, the frequency of the two waves must be the same. If the frequencies are different, the waves will not align and resonance will not occur.

## 3. What factors affect the amplitude of a standing wave?

The amplitude of a standing wave is affected by several factors, including the frequency, wavelength, and tension of the medium in which the wave is traveling. Additionally, the amplitude can be affected by any external forces acting on the medium.

## 4. How does resonance in standing waves impact musical instruments?

Resonance in standing waves plays a crucial role in the production of sound in musical instruments. When a musician plays a note on an instrument, the vibrations of the standing wave in the instrument's air column create a resonance that amplifies the sound and produces the desired tone.

## 5. Can resonance in standing waves be harmful?

While resonance in standing waves is a natural phenomenon, it can potentially be harmful in certain situations. For example, if an object is exposed to a standing wave with a frequency that matches its own natural frequency, it can cause the object to vibrate and potentially lead to structural damage. This is known as structural resonance and can be avoided by understanding the resonant frequencies of objects and avoiding exposure to matching standing waves.