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Chapter 17: Q.41 (page 485)

A violinist places her finger so that the vibrating section of a 1.0 g/m string has a length of 30 cm, then she draws her bow across it. A listener nearby in a 20°C room hears a note with a wavelength of 40 cm. What is the tension in the string?

Short Answer

Expert verified

The tension in the string is 265 N

Step by step solution

01

Write the given information

Length of the string, L= 30 cm =0.3m
The linear density of the string, µ = 1 g/m = 10-3 kg/m
Wavelength of the wave, λ = 40 cm = 0.4 m
The temperature of the room, T= 20°C

02

To determine the tension of the string 

The speed of sound at 20°C temperature, v = 343.3 m/s
The frequency of the sound wave is given by
f=vλf=343.30.4f=858.25Hz

The expression for the fundamental frequency of the string wave is given by
f=12LTµ858.25=12(0.3)T10-3858.25=10.6T10-3515=T10-32.65x105=T10-3T=265N
Thus, the tension in the string is 265 N

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