A string with a length of 4.00 m is held under a constant tension. The string has a linear mass density of μ = 0.006 kg/m. Two resonant frequencies of the string are 400 Hz and 480 Hz. There are no resonant frequencies between the two frequencies.
(a) What are the wavelengths of the two resonant modes?
(b) What is the tension in the string?

a) λn = 1.6m , λ(n+1) = 1.33

b) F(t) = 2457.6N

Explanation:

L = 4.0m

μ = 0.006kg/m

F1 =F(n) = 400Hz

F2 = F(n+1) = 480Hz

The natural frequencies of normal nodes for waves on a string is

F(n) = n(v / 2L)

F(n) = n / 2L √(F(t) / μ)

where F(t) = tension acting on the string

the speed (v) on a wave is dependent on the tension acting on the string F(t) and mass per unit length μ

v = √(F(t) / μ)

F(n) = frequency of the nth normal node

F(n+1) = frequency of the successive normal node.

frequency of thr nth normal node F(n) = n(v / 2L)equation (i)

frequency of the (n+1)th normal node F(n+1) = (n+1) * (v / 2L)equation (ii)

dividing equation (ii) by (i)

F(n+1) / F(n) = [(n+1) * (v / 2L)] / [n (v / 2L)]

F(n+1) / F(n) = (n + 1) / n

F(n +1) / Fn = 1 + (1/n)

1/n = [F(n+1) / Fn] - 1

1/n = (480 / 400) - 1

1/n = 1.2 - 1

1 / n = 0.2

n = 1 / 0.2

n = 5

the wavelength of the resonant nodes (5&6) nodes are

λ = 2L / n

λn = (2 * 4) / 5

λn = 8 / 5

λn = 1.6

λ(n+1) = (2 * 4) / (5 +1)

λ(n+1) = 8 / 6

λ(n+1) = 1.33m

b.

The tension F(t) acting on the string is

v = √(F(t) / μ)

v² = F(t) / μ

F(t) = μv²

but Fn = n(v / 2L)

nv = 2F(n)L

v = 2F(n)L / n

v = (2 * 400 * 4) / 5

v = 3200 / 5

v = 640m/s

substituting v = 640m/s into F(t) = v²μ

F(t) =(640)² * 0.006

F(t) = 2457.6N

the expression 15n + 2(3p) represents the amount isaiah spent buying gasoline and snacks, where n represents the price of each gallon of gasoline and p represents the cost of each snack that he bought. which statement is true about the amount isaiah spent?

nec chapter 5 contains

c. information on special occupancy areas

nec chapter 6 covers

a. special equipment

which of the following rules contain the words shall or shall not and must be adhered to?

b. mandatory rules

which of the following rules identify actions that are allowed but not required and typically cover options or alternative methods?

c. optional rules

which of the following serves as the introduction to the nec and provides an overview of the book?

a. nec article 90

organizations that test products for safety are

c. nrtls

the nec is published by the

a national fire protection association

the nec is divided into

b. 9 chapters

the nec provides informative annexes for

c. informational materials and examples

two terms from nec article 100 that trainees should become familiar with are

b. labeled and listed

explanation: