Waves Guitar
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what is the frequency of the sound wave produced by the guitar?
the string on a guitar is plucked so as to excite its third harmonic. the length of the string is 30 cm. the tension of the string is 100N and the linear mass density is 100g/m.
What is the frequency of the sound wave produced byt he guitar?
Explain the role of the guitar string and the guitar body in generating the sound wave?
Please show working!!
For a string fixed at each end resonances occur when the string length L (0.30m) is a multiple of ½ wavelengths (λ) between the end nodes ..
For the fundamental vibration (1st harmonic) L= ½ λ, between the end nodes ..
2nd harmonic L= 1λ ..
3rd harmonic L = 1.5λ, .. so λ = 0.30m / 1.5 .. .. 3rd harmonic λ = 0.20m ♦
Velocity of wave is given by equ. v = √(T/μ) .. (T= tension, 100N)(μ = mass density, 0.10kg/m)
v = √(100N / 0.01kg/m) = √1000 = 31.62 m/s ♦
Frequency F = v / λ = 31.62 / 0.20 .. .. ►F = 158 Hz (158.10)
The strings create the desired frequency, vibrations from the strings are transmitted to the guitar body through the bridge pieces (supporting the string ends and attached to the body). The large surface areas of the body are set vibrating at the same frequency as the string creating a louder sound than the string alone would make (and with it's own distinctive timbre - due to the waveform not being purely sinusoidal)
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