Question

To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.767 m ? (Assume that the breaking stress of the wire is very large and isn’t exceeded.)

Answer 1

Answer:

Tension, T = 547.58 N

Explanation:

It can be assumed that,

Mass of the string, m = 8.75 g

Length of the string, l = 70 cm = 0.7 m

Wavelength of produced sound, $\lambda=0.767\ m$

Speed of sound, v = 344 m/s

We know that second overtone is the third harmonic. The frequency in second overtone is given by :

$f=\dfrac{v}{3\lambda}$

$f=\dfrac{344}{3\times 0.767}$

f = 149.5 Hz

The frequency in terms of length is given by :

$f=\dfrac{1}{2l}\sqrt{\dfrac{T}{m/l}}$

$T=4f^2l^2\dfrac{m}{l}$

$T=4f^2lm$

$T=4\times (149.5)^2\times 0.7\times 8.75\times 10^{-3}$

T = 547.58 N

So, the tension in the string is 547.58 N. Hence, this is the required solution.