The six strings of a guitar are the same length under nearly the same tension, but they have different thicknesses. On which string do waves travel the fastest?
Correct answer: B. The thinnest string
- A. The thickest string
- B. The thinnest string
- C. The wave speed is the same on all the strings
- D. None of the above
Explanation
The velocity of a transverse wave in a stretched string is given by: v = √(T/n). Where T is the Tension and n is the mass per unit lenthn = m/L = ρπr^2/L where r is the radius of the wirer = d/2 where d is the diameterSo, v = √ (4T/ρπd^2)v= 2/d √(T/ρπ)As it can be seen, v is inversely proportional to dThus, the velocity of wave is highest for thinnest string.
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About Waves
Progressive waves transfer energy through oscillations, with wavelength, frequency, amplitude and wave speed related by v = fλ; sound speed depends on the medium. Superposition produces interference and stationary waves in strings and organ pipes, while simple harmonic motion describes the oscillation itself and must be distinguished from wave propagation.
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