Question

A streched string is forced to transmit transverse waves by means of an oscillator coupled to one end. The string has a diameter of 4mm. The amplititude of the oscillation is 10^(-4) m and the frequency is 10Hz. Tension in the string is 100 N and mass density of wire is 4.2xx10^(3)kg//m^3. Find (a) the equation of the waves along the string (b) the energy per unit volume of the wave (c) the average energy flow per unit time across any section of the string and (d) power required to drive the oscillator.

Answer 1

Answer:

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Explanation:

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Answer 2

Explanation:

• Radius = 2 mm
• Frequency f = 10 Hz
• A = 10^-4 m
• T = 100 N

Mass density = 4.2 x 10^3 Kg / m^3

μ = 4.2 x 10^3 x π ( 2 x 10^-3 )^2

v = √T / μ = √ 100 /  4.2 x 10^3 x π ( 2 x 10^-3 )^2

v = 43.5 m/s

k = ω / v = 2 π 10 / 43.5 = 1.44 m^-1

(a) Y = A sin ( Kx - ωt )

Y = 10^-4 sin ( 1.44 x - 2 πt )

(b) Energy density = 1/2 ρ A^2ω^2 = 1/2( 4.2 x 10^3 ) ( 10^-4)^2

Energy density = 8.29 x 10^-2 J/m^3

(c) Energy density x cross area = 8.29 x 10^-2 x π x ( 2 x 10^-3)^2

Energy density x cross area = 4.53 x 10^-5 J / s

(d) Power = 4.53 x 10^-5 J / s