The longitudinal displacement of sound wave

You have to convert the units of kx and ωt to match the argument of the cosine function. In summary, when considering a sound wave with a frequency of 330 Hz and a wavelength of 0.95 m, the displacement of an element of air located at x = 1.1 m and t = 0.12 s can be calculated using the formula s = sm cos (kx - ωt). By substituting the values of k and ω, we get a displacement of -7.625 µm. However, this is incorrect as the argument of the cosine function should be in radians, not degrees. Therefore, the units of kx and ωt need to be converted before
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Homework Statement



The longitudinal displacement of a mass element in a medium as a sound wave passes through it is given by s = sm cos (kx – ωt). Consider a sound wave of frequency 330 Hz and wavelength 0.95 m. If sm= 16 µm, what is the displacement of an element of air located at x = 1.1 m at time t = 0.12 s?

Homework Equations


k=2π/λ
ω=2πƒ
ƒ≡ frequency
ω≡ angular frequency
λ≡ wavelength
k≡ angular wave number

The Attempt at a Solution


substitute the values of λ and f in k and ω to get k=6.6138 m^-1 and ω=2073.45
∴ s= 16 cos ( 6.6138*1.1-2073.45*0.12)=-7.625 INCORRECT
Where I made mistake?
 
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  • #2
The argument of the cosine function is in what units? Radians or degrees?
 

FAQ: The longitudinal displacement of sound wave

What is the longitudinal displacement of sound wave?

The longitudinal displacement of sound wave refers to the distance that the particles of a medium move from their equilibrium position when a sound wave passes through it. It is a measure of the amplitude or intensity of the sound wave.

How is the longitudinal displacement of sound wave measured?

The longitudinal displacement of sound wave is measured in units of distance, such as meters or centimeters. It can be measured using instruments such as a microphone or a displacement detector, which can detect the changes in air pressure caused by the sound wave.

What factors affect the longitudinal displacement of sound wave?

The longitudinal displacement of sound wave is affected by the frequency, wavelength, and amplitude of the sound wave. It is also influenced by the properties of the medium through which the sound wave is traveling, such as density and temperature.

How does the longitudinal displacement of sound wave relate to the loudness of a sound?

The longitudinal displacement of sound wave is directly related to the loudness of a sound. This means that as the longitudinal displacement increases, the sound becomes louder, and as it decreases, the sound becomes quieter. This is why amplitude is often used as a measure of loudness.

Can the longitudinal displacement of sound wave be negative?

Yes, the longitudinal displacement of sound wave can be negative. This occurs when the particles of the medium move in the opposite direction of the sound wave, towards their equilibrium position. This is known as rarefaction and can be observed in the troughs of a sound wave.

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