Physics : Waves - Solved Example Problems for Stationary waves

Compute the distance between anti-node and neighbouring node.

For *nth* mode, the distance between anti-node and neighbouring node is

Let *f* be the fundamental frequency of the string. If the string is divided into three segments *l*1, *l*2 and *l*3 such that the fundamental frequencies of each segments be *f*1, *f*2 and *f*3, respectively. Show that

For a fixed tension *T* and mass density Âµ, frequency is inversely proportional to the string length i.e.

Consider a string in a guitar whose length is 80 cm and a mass of 0.32 g with tension 80 N is plucked. Compute the first four lowest frequencies produced when it is plucked.

The velocity of the wave

The length of the string, *L* = 80 cm=0.8 m The mass of the string, m = 0.32 *g* = 0.32 Ã— 10-3kg

Therefore, the linear mass density,

The tension in the string, *T* = 80 *N*

The wavelength corresponding to the fundamental frequency *f*1 is *Î»*1 = *2L* = 2 Ã— 0.8 = 1.6 m

The fundamental frequency *f*1 corresponding to the wavelength *Î»*1

Similarly, the frequency corresponding to the second harmonics, third harmonics and fourth harmonics are

*f*2* *= 2*f*1* *= 559 Hz

*f*3* *= 3*f*1* *= 838.5 Hz

*f*4* *= 4*f*1* *= 1118 Hz

Tags : Physics , 11th Physics : UNIT 11 : Waves

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