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# Solved Example Problems for Stationary waves

Physics : Waves - Solved Example Problems for Stationary waves

### EXAMPLE 11.20

Compute the distance between anti-node and neighbouring node.

### Solution

For nth mode, the distance between anti-node and neighbouring node is ### EXAMPLE 11.21

Let f be the fundamental frequency of the string. If the string is divided into three segments l1l2 and l3 such that the fundamental frequencies of each segments be f1f2 and f3, respectively. Show that ### Solution

For a fixed tension T and mass density µ, frequency is inversely proportional to the string length i.e. ### EXAMPLE 11.22

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.

### Solution

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 × 10-3kg

Therefore, the linear mass density, The tension in the string, T = 80 N The wavelength corresponding to the fundamental frequency f1 is λ1 = 2L = 2 × 0.8 = 1.6 m

The fundamental frequency f1 corresponding to the wavelength λ1 Similarly, the frequency corresponding to the second harmonics, third harmonics and fourth harmonics are

f2 = 2f1 = 559 Hz

f3 = 3f1 = 838.5 Hz

f4 = 4f1 = 1118 Hz

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