Calculating Fundamental Frequency and Wavelength of a Vibrating String

In summary, a 90 cm long steel string with a linear density of 1.1g/m and under 200N tension vibrates at a fundamental frequency of 7.49Hz. Converting the mass from grams to kilograms, the wavelength of the sound wave that reaches your ear in a 20 degree C room is 45.78m.
  • #1
cupcakequeen
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Homework Statement



A 90 cm long steel string with a linear density of 1.1g/m is under 200N tension. It is plucked and vibrates at its fundamental frequency. What is the wavelength of the sound wave that reaches your ear in a 20 degree C room?

Homework Equations



f = 1/2L * sqrt T/mu
v = f*gamma

The Attempt at a Solution


1/(2*0.9) * sqrt (200/1.1) = 7.49Hz
v = f*gamma so v/f = gamma; 343m/s/7.49 Hz = 45.78m
but this answer is wrong! Where did I go wrong?
 
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  • #2
metric units?
 
  • #3
yes, all metric
 
  • #4
what is the metric unit for mass?
 
  • #5
do I need to convert grams to kilograms?
 
  • #6
yup. thanks!
 

What is fundamental frequency?

Fundamental frequency, also known as the first harmonic, is the lowest frequency at which a periodic waveform repeats itself and is the building block of all other frequencies present in a complex sound.

How is fundamental frequency measured?

Fundamental frequency is typically measured in Hertz (Hz) or cycles per second and is determined by the rate of vibration of a sound source or the frequency of a sound wave.

What is the relationship between fundamental frequency and pitch?

Fundamental frequency and pitch are closely related, with the fundamental frequency being the physical measurement of the pitch of a sound. The higher the fundamental frequency, the higher the perceived pitch.

What factors can affect the fundamental frequency of a sound?

The fundamental frequency of a sound can be affected by various factors such as the size, shape, and tension of a sound source, as well as the medium through which the sound travels.

Why is fundamental frequency important in music and speech?

In music and speech, the fundamental frequency is crucial for conveying melody and intonation. It also helps in distinguishing between different voices and instruments, and can convey emotional cues in speech and music.

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