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Plane harmonic waves of frequency 500 Hz are produced in air with displacement amplitude 1 x 10-3 cm. Deduce pressure amplitude (in N/m2). (density of air = 1.29 gm/lit, speed of sound in air = 340m/s)
Correct answer is '13.8'. Can you explain this answer?
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Verified Answer
Plane harmonic waves of frequency 500 Hz are produced in air with disp...
Given A = 1 x 10-3 cm = 10-5 m, v = 500 Hz, v = 340 m/s, p = 1.29 g/lit = 1.29 kg/m3
Pressure amplitude
= 2 x 3.14 x 10-5 x 500 x 340 x 1.29
= 13.8 N/m2
The correct answer is: 13.8
Pressure amplitude
= 2 x 3.14 x 10-5 x 500 x 340 x 1.29
= 13.8 N/m2
The correct answer is: 13.8
Most Upvoted Answer
Plane harmonic waves of frequency 500 Hz are produced in air with disp...
Deducing the pressure amplitude in a plane harmonic wave requires the knowledge of the displacement amplitude and the properties of the medium in which the wave propagates. In this case, the wave is traveling in air, and we are given the displacement amplitude and the properties of air.
Given information:
- Frequency of the wave: 500 Hz
- Displacement amplitude: 1 x 10^(-3) cm
- Density of air: 1.29 gm/lit
- Speed of sound in air: 340 m/s
Let's go step by step to find the pressure amplitude.
1. Conversion of units:
First, we need to convert the displacement amplitude from centimeters to meters because the other quantities are given in SI units.
1 x 10^(-3) cm = 1 x 10^(-5) m
2. Angular frequency:
The angular frequency (ω) of the wave can be calculated using the formula:
ω = 2πf
where f is the frequency of the wave.
ω = 2π(500 Hz) = 1000π rad/s
3. Wavenumber:
The wavenumber (k) can be calculated using the formula:
k = ω/v
where v is the speed of sound in air.
k = (1000π rad/s) / (340 m/s) ≈ 9.24 rad/m
4. Relation between displacement and pressure:
The displacement (D) and pressure (P) amplitudes in a plane harmonic wave are related by the equation:
D = P/(ρω²)
where ρ is the density of the medium.
5. Rearranging the equation:
To find the pressure amplitude (P), we rearrange the equation:
P = Dρω²
6. Substituting values and calculating:
P = (1 x 10^(-5) m) * (1.29 kg/m³) * (1000π rad/s)²
P ≈ 13.8 N/m²
Therefore, the pressure amplitude of the wave is approximately 13.8 N/m².
Given information:
- Frequency of the wave: 500 Hz
- Displacement amplitude: 1 x 10^(-3) cm
- Density of air: 1.29 gm/lit
- Speed of sound in air: 340 m/s
Let's go step by step to find the pressure amplitude.
1. Conversion of units:
First, we need to convert the displacement amplitude from centimeters to meters because the other quantities are given in SI units.
1 x 10^(-3) cm = 1 x 10^(-5) m
2. Angular frequency:
The angular frequency (ω) of the wave can be calculated using the formula:
ω = 2πf
where f is the frequency of the wave.
ω = 2π(500 Hz) = 1000π rad/s
3. Wavenumber:
The wavenumber (k) can be calculated using the formula:
k = ω/v
where v is the speed of sound in air.
k = (1000π rad/s) / (340 m/s) ≈ 9.24 rad/m
4. Relation between displacement and pressure:
The displacement (D) and pressure (P) amplitudes in a plane harmonic wave are related by the equation:
D = P/(ρω²)
where ρ is the density of the medium.
5. Rearranging the equation:
To find the pressure amplitude (P), we rearrange the equation:
P = Dρω²
6. Substituting values and calculating:
P = (1 x 10^(-5) m) * (1.29 kg/m³) * (1000π rad/s)²
P ≈ 13.8 N/m²
Therefore, the pressure amplitude of the wave is approximately 13.8 N/m².
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Plane harmonic waves of frequency 500 Hz are produced in air with displacementamplitude1 x 10-3cm.Deduce pressure amplitude (in N/m2).(density of air = 1.29 gm/lit, speed of sound in air = 340m/s)Correct answer is '13.8'. Can you explain this answer?
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Plane harmonic waves of frequency 500 Hz are produced in air with displacementamplitude1 x 10-3cm.Deduce pressure amplitude (in N/m2).(density of air = 1.29 gm/lit, speed of sound in air = 340m/s)Correct answer is '13.8'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Plane harmonic waves of frequency 500 Hz are produced in air with displacementamplitude1 x 10-3cm.Deduce pressure amplitude (in N/m2).(density of air = 1.29 gm/lit, speed of sound in air = 340m/s)Correct answer is '13.8'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Plane harmonic waves of frequency 500 Hz are produced in air with displacementamplitude1 x 10-3cm.Deduce pressure amplitude (in N/m2).(density of air = 1.29 gm/lit, speed of sound in air = 340m/s)Correct answer is '13.8'. Can you explain this answer?.
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Plane harmonic waves of frequency 500 Hz are produced in air with displacementamplitude1 x 10-3cm.Deduce pressure amplitude (in N/m2).(density of air = 1.29 gm/lit, speed of sound in air = 340m/s)Correct answer is '13.8'. Can you explain this answer?, a detailed solution for Plane harmonic waves of frequency 500 Hz are produced in air with displacementamplitude1 x 10-3cm.Deduce pressure amplitude (in N/m2).(density of air = 1.29 gm/lit, speed of sound in air = 340m/s)Correct answer is '13.8'. Can you explain this answer? has been provided alongside types of Plane harmonic waves of frequency 500 Hz are produced in air with displacementamplitude1 x 10-3cm.Deduce pressure amplitude (in N/m2).(density of air = 1.29 gm/lit, speed of sound in air = 340m/s)Correct answer is '13.8'. Can you explain this answer? theory, EduRev gives you an
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