Question

A 64.0 cm long cord is vibrating in such a manner that it forms a standing wave with two antinodes. (The cord is fixed at both ends.) Which harmonic does this wave represent

Answer 1

Answer:

the wave represents the second harmonic.

Explanation:

Given;

length of the cord, L = 64 cm

The first harmonic of a cord fixed at both ends is given as;

$f_o = \frac{V}{2L}$

The wavelength of a standing wave with two antinodes is calculated as follows;

L = N---> A -----> N    +   N ----> A -----> N

Where;

N is node

A is antinode

L = N---> A -----> N    +   N ----> A -----> N =  λ/2  + λ/2

L = λ

The harmonic is calculated as;

$f = \frac{V}{\lambda} \\\\f = \frac{V}{L} = 2(\frac{V}{2L} ) = 2(f_o) = 2^{nd} \ harmonic$

Therefore, the wave represents the second harmonic.

L = λ