# Tension and frequency relationship

### Standing Waves on a String

Record the values for tension and length and the frequency of the tuning fork The relationship between the natural frequency of a stretched string and its. There is an equation relating the tension in a string fixed between two nodes and the velocity of the travelling waves which form the allowed. Arch Ital Biol. Jun;(3) Changes in tension-frequency relationship of motor units induced by their activity in rat muscle. Celichowski J(1) , Grottel.

The mode with the lowest frequency f1 is called the fundamental. Note that the nth mode has frequency n times that of the fundamental. All of the modes and the sounds they produce are called the harmonics of the string.

The frequencies f, 2f, 3f, 4f etc are called the harmonic series. This series will be familiar to most musicians, particularly to buglers and players of natural horns. If for example the fundamental is the note C3 or viola C a nominal frequency of Hz: These pitches have been approximated to the nearest quarter tone.

The octaves are exactly octaves, but all other intervals are slightly different from the intervals in the equal tempered scale. Double click on the top of column Y and rename fn. Enter in your values of the frequency for each n. Click on Analyze and Linear Fit to perform a linear fit of the data.

The slope of the graph is the measured value of the fundamental frequency, f1. The y-intercept, b, which should be zero, gives a measure of the uncertainty in your determination of the fundamental frequency. Record the fundamental frequency and uncertainty.

Compute the difference between the fundamental frequency and the slope. Calculate the wave velocity, v, two different ways. This lab is a specific demonstration of turning electrical energy into physical motion. What are some other examples of electrical energy being converted to physical motion? Why do we typically run this conversion?

Call over a TA or instructor and explain your conclusion to them. Relationship between Resonant Frequencies and Tension Using the same wire from part 1, hang a g weight from the wire. Double click on the top of column Y and rename f3 Enter in your values for frequency. What would the reversion of this conversion be? Can we do this conversion in real life?

If yes, what are some examples? If no, why can't we?

### PhysicsLAB: Relationship Between Tension in a String and Wave Speed

Vary the frequency until there are 3 anti-nodes. In the column for f3 enter in your values of the frequency. Click on Analyze and Linear Fit to perform a linear fit of the data From eq.

Record the value of the slope. Calculate the expected value of the slope. Now that you have experimented with the number of nodes, the tension and the mass per unit length, consider this hypothetical situation: Near a node, the oscillation amplitude is very small. In the middle of the string, the oscillation amplitude is largest; such a position is defined as an antinode.

We assign a wavelength to the fundamental and each higher harmonic discussed below standing wave. At a fixed moment in time, all we observe is either a crest or a trough, but we never observe both at the same time for the lowest frequency standing wave.

From this, we determine that half a standing wave length fits along the length of the string for the fundamental. Alternatively, we say that the wavelength of the fundamental is twice the length of the string, or As we'll discuss later, the oscillation frequencies of stretched strings effect the tone of the sounds we hear from instruments such as guitars, violins and cellos.

Higher frequency oscillations result in higher-pitched tones; lower frequency oscillations produce lower-pitched tones. So how can we change the oscillation frequency of a stretched string? The above equation tells us. If we either increase the wave speed along the string or decrease the string length, we get higher frequency oscillations for the first and higher harmonic.

Conversely, reducing the wave speed or increasing the string length lowers the oscillation frequency. How do we change the wave speed? Keep in mind, it is a property of the wave medium, so we have to do something to the string to alter the wave speed.

From earlier discussions, we know that tightening the string increases the wave speed. We also know that more massive strings have smaller wave speeds.

## String vibration

As an example of how standing waves on a string lead to musical sounds, consider the first harmonic of a G string on a violin. The diameter of the G string is 4 mm.

**Wave Speed on a String, Tension, Intensity, Power, Amplitude, Frequency - Inverse Square Law Physics**

The string is held with a tension of N. The frequency of the first harmonic of the G string is Hz.

What is the length of the string? Higher harmonics Higher harmonics within the harmonic series come from successively adding nodes fixed points, where the string doesn't move to the standing wave pattern. Every time there is an additional node, the frequency gets higher.