Question

(a) what is the displacemant amplitude for a sound wave having a frequency of 100 Hz and a pressure amplitude of 10 pa? (b) The displacement amplitude of a sound wave of frequency 300 Hz is 10^(-7) m. what is the pressure amplitude of this wave ? speed of sound in airb is 340 ml s and density of a ir is 1.29kg// m^(3).

Answer 1

Given: Frequency of sound wave = 100Hz

Another frequency = 300Hz

To Find: Displacement amplitude and speed of sound

Solution: (Δp)m = BAk  

where k = ω/ν = 2πf/ν  

Also, B = ρν² (asν = √B/ρ

Therefore,

(Δp)m = (ρν²)(A)(2πf/ν)  

Thus,

A=(Δp)m/2πνρf

Substituting the values -  

A = 10 / 2 × 3.14 × 340 × 1.29 × 100  

= 3.63 × 10`−5m  

(b) (Δp)m=2πfρνA

Substituting the values -  

(Δp)m = 2 × 3.14 × 300 × 1.29 × 340 × 10`−7  

Answer : 8.26×10²m²