Question

A standing wave is established on a string that is fixed at both ends.

If the string is vibrating at its fundamental frequency, how is the length of the string related to the wavelength of the standing wave?

a. The length of the sting is equal to one-quarter of a wavelength.
b. The length of the string is equal to the wavelength.
c. The length of the string is equal to twice the wavelength.
d. The length of the string is equal to one-half of a wavelength.
e. The length of the string is equal to four times the wavelength.

Answer 1

d)The length of the string is equal to one-half of a wavelength (L = λ/2)

Step-by-step explanation:

When a standing wave is established on string which is fixed at both ends,

Then the relation between length of the string and wavelength is given by

L = λ/2

In this scenario, the length of the string is equal to one-half of the wavelength.

Another possible case is when on end of the string is fixed and one end of the string is free, in such case, the length of the string is equal to one-quarter of the wavelength.

Answer 2

d. The length of the string is equal to one-half of a wavelength.

Step-by-step explanation:

For a standing waves vibrating with Fundamental Frequency will be vibrate in one loop so Length 2 L = λ ⇒ L = 1/2 λ