Question

A standing wave is set up in a L=2.00m long string fixed at both ends. The string vibrates in its 5th harmonic when driven by a frequency f=120Hz source. The mass of the string is m=3.5grams. Recall that 1kg = 1000grams.

A. Find the linear mass density of the string

B. What is the wavelength of the standing wave

C. What is the wave speed

D. What is the tension in the string

E. what is the first harmonic frequency f1 of the string?

Answer 1

Part A)   

Linear mass desnity = mass/ length = 3.5/2 = 1.75 gm/ m of 0.00175 kg/m

Part B)

Wavelength of nth harmonic = 2 L / n so Wavelength of 5th harmonic = 2 L / 5 = (2 * 2) / 5 = 0.8 m

Part C)

Wave speed of nth harmonic = Frequency of nth harmoninc * Wavelenth = 120 *0.8 = 96 m/s

Part D)

Tenson of string = velocity² * Linear mass density = 96 ² * 0.00175 kg/m = 16.128 N

Part E)

First harmonic frequency = 1/2L T/M = 1 / ( 2 *2) (16.128 / 0.00175) = 0.25 * 9216 = 0.25 *96 = 24