Question

A string with a length of 0.75 m is fixed at both ends. (a) What is the longest possible wavelength for the traveling waves that can interfere to form a standing wave on this string? (b) If waves travel with a speed of 130 m/s on this string, what is the frequency associated with this longest wavelength?

Answer 1

a) Longest wavelength is:
`\lambda_(1)=2*0.75=1.5\: m`

b) The frequency associated with this longest wavelength is:
`f=86.7\: Hz`

Step-by-step explanation:

a)

The wavelength equation of a standing wave is given by:

`\lambda_(n)=(2)/(n)L`

Where:

• L is the length of the string
• n is a natural number

We use n=1 to find the longest possible wavelength, so we will have:

`\lambda_(1)=2L`

`\lambda_(1)=2*0.75=1.5\: m`

b)

The speed of the wave is given by:

`v=f\lambda`

So we just need to find the f (frequency).

`f=(v)/(\lambda)`

`f=(130)/(1.5)`

`f=86.7\: Hz`

I hope it helps you!