(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).
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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
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