Question

A cellist tunes the C string of her instrument to a fundamental frequency of 65.4 Hz. The vibrating portion of the string is 0.590 m long and has a mass of 15.0 g.
(a) Calculate the wavelength corresponding to this fundamental frequency?
(b) Calculate the wave speed.
(c) With what tension must the musician stretch the string?

Answer 1

Answer:

a

$\lambda = 1.18 \ m$

b

$v = 77.172 \ m/s$

c

$T = 151.41 \ N$

Explanation:

From the question we are told that

   The frequency is  $f = 65.4 \ Hz$

   The  length of the vibrating string is  $L = 0.590 \ m$

   The  mass is  $m = 15.0 \ g = 0.015 \ kg$

Generally the wavelength is mathematically represented as

           $\lambda = 2 * L$

=>        $\lambda = 2 * 0.590$

=>         $\lambda = 1.18 \ m$

Generally the wave speed is  

          $v = \lambda * f$

=>       $v = 1.18 * 65.4$

=>       $v = 77.172 \ m/s$

Generally the tension on the wire is mathematically represented as

        $T = v^2 * \frac{ m }{L }$

=>      $T = 77.172 ^2 * \frac{ 0.015 }{0.590}$

=>      $T = 151.41 \ N$