Conceptual Physics

There is only one solution to the problem we pose, given the range of string lengths and harmonics together with the wave speed we provide.

If you are not sure how to proceed, try solving the equation above for the string length and entering the known values. You will still have

another variable, n, left in the equation. However, since you know the range of string lengths, and that n must be an integer from one to four,

you will be able to solve the problem.

To test your answer, set a string length and harmonic number and press GO to see a hand come down and pluck the string so you can hear

the resulting note and see its frequency. The resulting musical note is displayed on the sounding board. Press RESET to start over.

17.6 - Sample problem: string tension

The values shown in the problem are representative of the lowest frequency string on a guitar. To answer the question, you must first

determine the harmonic of the standing wave. You can do so by inspecting the diagram above. We exaggerated the amplitude of the wave to

make the nodes and antinodes more visible.

Variables

What is the strategy?

1. Determine the harmonic by counting the number of nodes shown in the string above.


2. Calculate the wave speed from the frequency, string length and harmonic number.


3. Calculate the tension using the equation for wave speed on a string.

Physics principles and equations

Nodes are locations where there is no displacement. The harmonic number is one less than the number of nodes, including the nodes at the

ends of the string.

The equation for the nth harmonic

The wave speed on a stretched string

The frequency of the standing wave

on the string is 329 Hz. What is the

tension on the string?

string length L = 0.640 m

string mass m = 0.00435 kg

frequency ƒ = 329 Hz

harmonic number n

wave speed v

tension T

(^328) Copyright 2000-2007 Kinetic Books Co. Chapter 17