A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. It is vibrating in its third overtone, and the equation for the vertical displacement of any point on the string is y(x,t) = (1.19 cm) sin[(13.7 m-1)x] cos[(103 rad/s)t]. What is the fundamental frequency of the string (in Hz)?
Properties of sound
A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).
Quality Of Sound
A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.
Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
1. A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. It is vibrating in its third overtone, and the equation for the vertical displacement of any point on the string is y(x,t) = (1.19 cm) sin[(13.7 m-1)x] cos[(103 rad/s)t]. What is the fundamental frequency of the string (in Hz)?
2. A guitar string 0.625 m long has a tension of 61.1 N and a mass per unit length of 2.27 g/m. What is the string's fundamental frequency (in Hz) of vibration when plucked?
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