# Calculating Next 3 Harmonics of a Standing Wave

• Nano
In summary: The wave speed c is the same for all frequencies, and as you say, c = f \lambda This should be enough for you to deduce the frequencies and the wavelengths of the harmonics (or overtones as they are sometimes called).So as I've said that the wavelength of the first harmonic =(4/3)L, that means the wavelength of the second harmonic = (4/3)L / n = (4/3)L / 2 = (2/3) L
Nano

## Homework Statement

Given the first harmonic, with length L, of a certain standing wave, what is the process for coming up with the next 3 harmonics for it?

## Homework Equations

velocity = wavelength * frequency

## The Attempt at a Solution

I don't understand how to draw the "next harmonic". I've come up with a formula for wavlenth of the first harmonic:
= (4/3)L
and with that, frequency
= (3v)/(4L)

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Take a butchers at this...

http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html"

Last edited by a moderator:
Nano said:

## Homework Statement

Given the first harmonic, with length L, of a certain standing wave, what is the process for coming up with the next 3 harmonics for it?

## Homework Equations

velocity = wavelength * frequency

## The Attempt at a Solution

I don't understand how to draw the "next harmonic". I've come up with a formula for wavlenth of the first harmonic:
= (4/3)L
and with that, frequency
= (3v)/(4L)

Well, for a standing wave the ends are fixed and therefore are nodes. In a sinusoidal wave the nodes are half a wavelength apart. In a string of length L, standing vibrations may be set up by different frequencies that give rise to waves that will have nodes at the endpoints. These wave will have wavelengths,

$$\lambda = 2L, \frac{2L}{2}, \frac{2L}{3},..., \frac{2l}{n}$$

The wave speed c is the same for all frequencies, and as you say, $$c = f \lambda$$

This should be enough for you to deduce the frequencies and the wavelengths of the harmonics (or overtones as they are sometimes called).

So as I've said that the wavelength of the first harmonic =(4/3)L, that means the wavelength of the second harmonic
= (4/3)L / n = (4/3)L / 2 = (2/3) L

Is this right?

By the way, the wave has a node at one end and is open at the other. In class we learned that standing waves with one open/one fixed end have only odd numbered harmonics. Why is this?

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## 1. How do you calculate the next 3 harmonics of a standing wave?

The next 3 harmonics of a standing wave can be calculated by multiplying the fundamental frequency by 2, 3, and 4 respectively. The resulting values will be the second, third, and fourth harmonics of the standing wave.

## 2. What is a standing wave?

A standing wave is a type of wave that remains in a constant position, oscillating back and forth between two points. It is formed when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other.

## 3. Why is it important to calculate the harmonics of a standing wave?

Calculating the harmonics of a standing wave is important because it allows us to understand the properties and behavior of the wave. The different harmonics determine the overall shape and stability of the standing wave and can also have practical applications in fields such as acoustics and electromagnetic radiation.

## 4. What is the formula for calculating the next harmonic of a standing wave?

The formula for calculating the next harmonic of a standing wave is Hn = nF, where Hn is the harmonic, n is the number of the harmonic (2, 3, 4, etc.), and F is the fundamental frequency of the standing wave.

## 5. Can the next 3 harmonics of a standing wave be different from each other?

Yes, the next 3 harmonics of a standing wave can be different from each other. The harmonics are determined by the fundamental frequency and the number of the harmonic, so each one will have a unique value. However, they will all have a relationship to the fundamental frequency and will follow the same pattern of increasing by a factor of 2, 3, and 4 respectively.

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