An investigation into the factors affecting the frequency of a standing wave

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An investigation into the factors affecting the frequency of a standing wave

Introduction

There are several ways in which you can control the pitch (frequency) of a note produced by a string.

A string with 2 fixed ends (called nodes) can produce different standing waves. The lowest frequency standing wave that can be produced has a wavelength λ where

                        λ = 2ℓ   (ℓ = length of string)

This is related to the frequency ƒ of oscillation by the wave equation

                        V = ƒλ

Where V is the speed of transverse waves traveling along the string. You can therefore deduct that

                        ƒ = v/λ = v/2ℓ

ƒ therefore should be inversely proportional to the length of the string, i.e. the shorter the string, the higher the note.

The frequency will also depend on the tension and the mass per unit length of the string, as they affect the speed of transverse waves traveling along the string. The greater the tension, the greater the speed, and the heavier the string, the lower the speed.

This becomes important in this investigation because if the experiment is to be fair, then the two other factors affecting the frequency must be kept constant for the results to be accurate.

I have decided to investigate the effect that altering the length of string along which the wave travels. From the above equations, I would expect the frequency to be inversely proportional to the length of string, as you would create a shorter wavelength when the string is shorter, and the speed can be kept constant.

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Because I am only investigating the change in frequency caused by a change in length of the string, both the tension and the mass per unit length of the strength need to be kept the same to get accurate results.

Method

To keep the Mass per unit length of wire the same, I am going to use the same piece of constantan wire for all my results, which has a mass per unit length of 32 (swp). The tension can also be controlled by using a constant mass suspended from one end of the wire.

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This is a well written report that lacks structure. 1. There are several subheadings missing. 2. The table of results needs to be included. 3. The conclusion needs to quote data from the investigation. 4. The evaluation needs to suggest further opportunities. ****