A string is fixed at both ends and vibrating at 140 Hz, which is its third harmonic frequency. The linear density of the string is 4.6x10-3 kg/m, and it is under a tension of 2.3 N. Determine the length of the string.

Length of the string = 0.24 m

Explanation:

The frequency (f) of vibration of stringed instruments is related to the Tension (T) in the spring by the relation

fₙ = (n/2L)√(T/μ)

where n = 1,2,3,4...

For third harmonic frequency, n = 3

L = length of the string = ?

T = tension in the string = 2.3 N

μ = linear density = 4.6 × 10⁻³ kg/m

f = frequency = 140 Hz

L = (n/2f)√(T/μ)

L = (3/(2×140))√(2.3/0.0046) = 0.40 m

Explanation:

Below is an attachment containing the solution

answer: the correct answer for the fill in the blank is rods.

rods are the specialized photoreceptor cells that are present in the retina of human eye. they are responsible for vision in the night time ( also called scotopic vision). they have very low visual acuity and color distinguishing ability.

as they are responsible for vision in night time, therefore they are found predominantly in the nocturnal animals.