A thin 2 m long string with mass 10 g is stretched between two ends. The string vibrates in the second harmonic which has frequency 50 Hz, and the amplitude of the oscillations is 3 cm. The speed of sound is approximately 350 m/s

a) What is the tension in the string?

b) What is the maximum transverse speed and acceleration of the node and the antinode?

c) What is the wavelength of sound waves produced by these string vibrating?

Answer: (a). Tension = 612.5 N

(b). Maximum transverse speed = 9.42m/s

acceleration of node and antinode = 2957.88 m/s²

(c). wavelength = 7m

Explanation:

ok to begin,

we would define the parameters given;

the length L = 2m

mass M = 10g = 10*10⁻³kg

frequency F = 50Hz

speed of sound V = 350 m/s

amplitude A = 3cm = 0.03m

(a). from formula;

V = √ (T/μ) ... (1)

where μ = linear mass density which is given as

μ = m/L = 10⁻² / 2 = 0.5*10⁻² kg/m

from equation 1,

V² = T/μ

T = V² * μ

T = 350²*0.5*10⁻²

T = 612.5 N

(b). to solve the for the maximum speed;

Vmax = AW

Vmax = A * 2πf

Vmax = 0.03 * 2π * 350

Vmax = 9.42m/s

(ii). the general form for the maximum transverse acceleration of the node and antinode is given as;

Am = W² * ym

= (2π50) ² * 0.03

Am = 2957.9 m/s²

(c) wavelength of the sound is given;

V = Fλ

where λ = V/F

λ = 350 / 50

λ = 7m