Q.41 A violinist places her finger so... [FREE SOLUTION]

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掳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

Write the given information

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

To determine the tension of the string

The speed of sound at 20掳C temperature, v = 343.3 m/s
The frequency of the sound wave is given by
$f = \frac{v}{位} f = \frac{343.3}{0.4} f = 858.25 H z$

The expression for the fundamental frequency of the string wave is given by
$f = \frac{1}{2 L} \sqrt{\frac{T}{碌}} 858.25 = \frac{1}{2 (0.3)} \sqrt{\frac{T}{10^{- 3}}} 858.25 = \frac{1}{0.6} \sqrt{\frac{T}{10^{- 3}}} 515 = \sqrt{\frac{T}{10^{- 3}}} 2.65 x 10^{5} = \frac{T}{10^{- 3}} T = 265 N$
Thus, the tension in the string is 265 N