Question

The tension in a string is 15 N, and its linear density is 0.85 kg/m. A wave on the string travels toward the −x direction; it has an amplitude of 3.6 cm and a frequency of 12 Hz.

(a) What are speed and wavelength of the wave?
(a) Write down the mathematical expression for the wave.

Answer 1

a) v = 4.20 m/s, 0.35 m

b) y = 0.036sin(24πt + 17.94x)

Step-by-step explanation:

Given:

Tension in the string, T = 15 N

Linear density of the string, M = 0.85 kg/m

Amplitude of the wave, A = 3.6 cm = 0.036 m

Frequency of the wave, f = 12 Hz

a) now,

the speed (v) of the wave is given as:

v = √(T/M)

on substituting the values, we get

v = √(15/0.85)

or

v = 4.20 m/s

also, wavelength (λ) is given as:

λ = v/f

on substituting the values, we get

λ = 4.20/12

or

λ = 0.35 m

b) The mathematical expression for the wave is given as:

y = Asin(2πft + (2π/λ)x)

thus,

on substituting the values, we get

y = 0.036sin(2π×12×t + (2π/0.35)x)

or

y = 0.036sin(24πt + 17.94x)