Standing waves and vibration frequency

AI Thread Summary
To find the tension in the string, first note that the vibrating length of the string is 30 cm, which corresponds to a wavelength of 40 cm in air. The frequency of the sound heard is equal to the vibration frequency of the string, calculated using the speed of sound in air (343 m/s) and the wavelength. The wave speed in the string can be determined from the tension and linear density. By applying the relationship between wave speed, tension, and density, the tension in the string can be calculated. This method effectively combines the principles of wave mechanics and string vibration.
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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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
 

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