Question

Cousin Throckmorton is playing with the clothesline. One end of the clothesline is attached to a vertical post. Throcky holds the other end loosely in his hand, so that the speed of waves on the clothesline is a relatively slow 0.700 m/s . He finds several frequencies at which he can oscillate his end of the clothesline so that a light clothespin 40.0 cm from the post doesn't move. What are these frequencies?

Answer 1

The frequencies are
`f_n = n (0.875 )`

Step-by-step explanation:

From the question we are told that

The speed of the wave is
`v = 0.700 \ m/s`

The length of vibrating clothesline is
`L = 40.0 \ cm = 0.4 \ m`

Generally the fundamental frequency is mathematically represented as

`f = (v)/(2 L )`

=>
`f = ( 0.700 )/(2 * 0.4 )`

=>
`f = 0.875 \ Hz`

Now this other frequencies of vibration experience by the clotheslines are know as harmonics and they are obtained by integer multiple of the fundamental frequency

So

The frequencies are mathematically represented as

`f_n = n * f`

=>
`f_n = n (0.875 )`

Where n = 1, 2, 3 ....