A certain stretched string has a fundamental frequency for standing transverse waves of 440 Hz. The tension in the string is then increased by 21%. This tension increase changes the fundamental frequency to
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.
Initial fundamental frequency = n = 440 Hz
Total tension after it increased by 21 % = T' = T + 0.21T = 1.21T
New fundamental frequency = n' =?
Here, we are using the same string, therefore the values of length (l), linear density (m) of the string are constant in both cases.
The fundamental frequency is
. . . . . (i)
Where,
length of string = l
Tension in string = T
linear density of string = m
The new fundamental frequency after increasing the tension is
Substituting T'= 1.21T
. . . . . (ii)
Divide equation (ii) by equation (i),
Substituting the values,
484 Hz
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