The A string on a cello vibrates in its first normal mode with a frequency of 220 Hz. The vibrating segment is 70.0 cm long and has a mass of 1.20 g. (a) Find the tension in the string. (b) Determine the frequency of vibration when the string vibrates in three segments

Force is 161.27 N and frequency of vibration when the string vibrates in three segments is 660 Hz .

Explanation:

Given :

Frequency , f = 220 Hz .

Length of wire , L = 70 cm = 0.7 m .

Mass of wire ,

a ) We know, frequency in string is :

Therefore ,

   .... equation 1.

Here , is mass per unit length .

So,

Putting value of in equation 1.

We get ,

b) We know , frequency of when n segment are in string :

For , n = 3

Hence , this is the required solution.

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