A cello string vibrates in its fundamental mode with a frequency of 168 1/s. The vibrating segment is 86.7 cm long and has a mass of 0.55 g. Find the tension in the string. Answer in units of N. Find the frequency of the string when it vibrates in two segments. Answer in units of 1/s.

Tension = 0.034 N

Frequency in two segments = 336 1/s

Explanation:

The frequency of a string is given by

k represents the mode of vibration; for the fundamental frequency, k = 1

l is the length of the string in metre

T is the tension of the string in newton

is the linear density or mass per unit length in kg/m; it is a measure of the thickness of the string

Making T the subject of the formula,

f = 168

l = 86.7 cm = 0.867 m

Then

When the string vibrates in two segments, it is in the second harmonic. This is simply twice the fundamental frequency.

Hence, f = 2 × 168 = 336 1/s

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