Standing waves and vibration frequency

Hey there! In summary, a violinist draws her bow across a 1.0g/m string with a length of 30cm, producing a sound with a wavelength of 40cm at a temperature of 20 degrees celcius. The tension in the string can be calculated using the relationship between frequency, wavelength, speed, tension, and density. This can be helpful in determining the tension of a string in similar situations. Good luck on your exam!
  • #1
bigsaucy
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A violinist places her finger so that the vibrating section of a 1.0g/m string has a length of 30cm, then she draws her bow across it. A listener nearby in a 20 degrees celcius room (speed of sound at this temperature in air is 343 m/s) hears a note with a wavelength of 40 cm. What is the tension in the string?


I was having real trouble with this question. I have an exam in 4 hours, any help would be greatly appreciated!
 
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  • #2
The vibration frequency of the string is the same as that of the sound heard in air. The wavelength of the elastic wave in the string is related to the vibrating length of the string. The wavelength is related to the frequency and the speed of the wave. Speed of the wave in the sting is related to tension and density. Put all that together.


ehild
 

What are standing waves and how are they formed?

Standing waves are a type of wave that forms when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. The resulting pattern appears to be a stationary wave, with nodes and antinodes that do not move.

What is the relationship between standing waves and vibration frequency?

The vibration frequency of a standing wave is directly related to the wavelength of the wave and the length of the medium it is traveling through. The frequency of the standing wave is equal to the velocity of the wave divided by twice the length of the medium.

How do standing waves affect the sound produced by a musical instrument?

In musical instruments, standing waves are responsible for the production of different notes. The length of the instrument's air column determines the wavelength of the standing wave and thus the frequency of the sound produced. By altering the length of the air column, different notes can be produced.

What factors can affect the formation of standing waves?

The formation of standing waves can be affected by the properties of the medium through which the waves are traveling. These include the speed of the wave, the length of the medium, and any obstructions or boundaries that the waves encounter.

How are standing waves used in real-world applications?

Standing waves have a variety of applications in different fields. In music, they are used in instruments such as guitars and flutes to produce different notes. In physics, they are used to study the properties of materials and to measure vibration frequencies. They are also used in medical imaging techniques, such as ultrasound, to create images of internal body structures.

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