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

Answer:

a) Longest wavelength is: $\lambda_{1}=2*0.75=1.5\: m$

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

Explanation:

a)

The wavelength equation of a standing wave is given by:

$\lambda_{n}=\frac{2}{n}L$

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).

$f=\frac{v}{\lambda}$

$f=\frac{130}{1.5}$

$f=86.7\: Hz$

I hope it helps you!