Solve Standing Wave Problem: Fundamental Frequency & Tension of String

In summary, the problem involves a violinist playing a string with a length of 30 cm and a listener hearing a note with a wavelength of 40 cm. The goal is to determine the tension in the string using the equation for fundamental frequency. The issue is figuring out the speed of the wave on the string, which depends on the tension of the string. One suggestion is to assume the speed of sound in air based on the given temperature to calculate the frequency and then solve for tension.
  • #1
physstu
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Hi, I have been staring at this problem for 2 hours now, and I feel like it is really simple, but I cannot quite wrap my head around it...here it is

A violinist places her finger so that the vibrating section of her 1.0 g/m string has a length of 30 cm, then she draws her bow across it. A listener nearby in a 20 degrees C room hears a note with a wavelength of 40 cm. What is the tension in the string?


I have been messing around with a couple different equations. The one I am pretty sure I need to use is:

Fund. Freq. = v/2L = 1/2L * [tex]\sqrt{T_{s}/linear density}[/tex]

So I figured if I could somehow get v (speed of the wave on the string) or the fundamental frequency, I could solve for the tension of the string. This is where the problem is I have no idea how to do that, because as far as i know the speed of a wave on a string depends on the Tension of the string, which brings us back to what we need in the first place...

Any advice at all would be appreciated because I am really stumped.
Thanks!
 
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  • #2
I think you have to make an assumption about the speed of sound in air, base don the given temperature...

This will give you the frequency, form which you should be able to get tension
 

What is a standing wave?

A standing wave is a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This creates a stationary pattern of nodes and antinodes, where the amplitude of the wave remains constant at specific points.

How do you solve a standing wave problem?

To solve a standing wave problem, you need to know the fundamental frequency and tension of the string. You can determine the fundamental frequency by dividing the wave speed by twice the length of the string. The tension of the string can be found using the equation T = (m * v^2) / L, where T is tension, m is mass per unit length, v is wave speed, and L is the length of the string.

What is the fundamental frequency of a string?

The fundamental frequency of a string is the lowest frequency at which a standing wave can occur. It is also known as the first harmonic and is determined by the length, mass per unit length, and tension of the string. The fundamental frequency is an important factor in determining the pitch of a musical instrument.

How does tension affect the standing wave on a string?

Tension is a crucial factor in determining the fundamental frequency of a string. As tension increases, the fundamental frequency also increases. This means that a string with higher tension will produce a higher-pitched sound. Additionally, higher tension can also result in more nodes and antinodes, creating a more complex standing wave pattern.

What are some real-life applications of standing waves?

Standing waves have many practical applications in science and technology. They are used in musical instruments to produce different pitches and in telecommunications to transmit signals over wires. Standing waves can also be observed in natural phenomena, such as ocean waves and seismic waves. In addition, they play a significant role in the study of quantum mechanics and the behavior of particles at the subatomic level.

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