What is the speed of sound and tension in a vibrating harpsichord string?

In summary, a harpsichord string with a length of 1.60 m and linear mass density of 25.0 mg/m has a fundamental frequency of 450.0 Hz. Using the equation v=2Lfn/n, we can calculate the speed of the transverse string waves to be 1440 m/s. To find the tension, we can use the equation v = \sqrt{\frac{T}{\mu}}, where T represents tension and \mu represents linear mass density. Finally, to find the wavelength and frequency of the sound wave produced by the string, we need to consider the speed of sound in air, which is 340 m/s at room temperature. The frequency of the sound wave would also
  • #1
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Homework Statement


A harpsichord string of length 1.60 m and linear mass density 25.0 mg/m vibrates at a (fundamental) frequency of 450.0 Hz.
(a) What is the speed of the transverse string waves?

(b) What is the tension?

(c) What are the wavelength and frequency of the sound wave in air produced by vibration of the string? The speed of sound in air at room temperature is 340 m/s.



Homework Equations



v=2Lfn/n

The Attempt at a Solution


Already used above equation to find the speed, 1440 m/s. Not sure how to find part b or c though
 
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  • #2
You're missing a relevant equation that relates tension of the string to the speed of a wave and the linear mass density of the string. This is given by

[tex]
v = \sqrt{\frac{T}{\mu}}
[/tex]

Try working with that and see if you can get the rest.
 
  • #3
For (c): what must the frequency of the sound be?
 

1) What is fundamental frequency?

Fundamental frequency, also known as the first harmonic, is the lowest frequency of a periodic waveform. It is the base frequency that determines the pitch of a sound.

2) How is fundamental frequency measured?

Fundamental frequency is measured in Hertz (Hz) and can be determined using a frequency analyzer or by counting the number of cycles per second in a waveform.

3) What factors affect the fundamental frequency of a sound?

The fundamental frequency of a sound is affected by the physical properties of the sound source, such as the length, tension, and density of the vibrating object. It can also be affected by the environment and any obstructions that may alter the sound waves.

4) Can fundamental frequency change in a sound?

Yes, the fundamental frequency can change in a sound. This can be caused by changes in the physical properties of the sound source or by altering the shape or characteristics of the sound waves through techniques such as modulation or filtering.

5) Why is fundamental frequency important?

Fundamental frequency is important because it is the primary factor that determines the pitch of a sound. It is also used in music theory to understand and classify different musical notes and intervals. In addition, changes in fundamental frequency can convey emotion and meaning in spoken language, making it a crucial aspect of communication.

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