Answer to Question #273147 in Optics for agumar

Question

A wire of length 3.45 m and mass 13.70 g is under a tension of 1.25 N. A standing wave has formed which has seven nodes excluding the endpoints. Calculates the frequency of this wave?

Answer 1

The number of harminic is $n = 7+1 = 8$, since the first harmonic has 0 nodes excluding the endpoints. The frequency is given as follows:

$$f_n = \dfrac{nv}{2L}$$

where $L = 3.45m$ and $v$ is the speed of the wave. $v$ is given as follows:

$$v = \sqrt{\dfrac{FL}{m}}$$

where $F = 1.25N, m = 13.70g = 0.01370kg$. Thus, obtain:

$$f_n = \dfrac{n}{2L}\sqrt{\dfrac{FL}{m}} =\dfrac{n}{2}\sqrt{\dfrac{F}{Lm}} \\ f_8 = \dfrac{8}{2\cdot}\cdot \sqrt{\dfrac{1.25}{ 3.45\cdot 0.01370}} \approx 20.6Hz$$

Answer. 20.6 Hz.