# Longitudinal Waves - are they very different?

• Stealth849
In summary, a continuous sinusoidal longitudinal wave with a frequency of 25vib/sec and a distance of 24cm between successive rarefactions travels along a coil spring with a wave speed of 6m/s. The maximum longitudinal displacement of a particle is 3.0cm, and the equation for the wave is D(x,t) = 0.03sin(2∏x/0.24 + 50∏t). This equation is appropriate for modeling longitudinal waves, such as sound waves or pressure waves in solids.
Stealth849

## Homework Statement

A continuous sinusoidal longitudinal wave is sent along a coil spring from a vibrating source attached to it. The frequency of the source is 25vib/sec, and the distance between successive rarefactions in the spring is 24cm.

a) Find the wave speed

b) if the max longitudinal displacement of a particle in the spring is 3.0cm, and the wave moves in the -x direction, write the equation for the wave. Let the source be at x = 0, and displacement at x = 0 and t = 0 be zero.

## Homework Equations

v = λf

k = 2∏/λ

ω = 2∏f

D(x,t) = Asin(kx - ωt)

## The Attempt at a Solution

Just looking for some clarification on everything here - the fact that it is a longitudinal wave kind of freaks me out a bit, but it should be able to be modeled the same as a transverse wave right?

v = λf = 0.24*25 = 6m/s

then to model the wave...

Amplitude should be the maximum displacement of a particle, 0.03m

k = 2∏/λ = 2∏/0.24
ω = 2∏f = 50∏

D(x,t) = Asin(kx+ωt) = 0.03sin(2∏x/0.24 + 50∏t)

Is this equation correct for this longitudinal wave?
Thanks

Yes, that all looks correct. (Sound waves are longitudinal too, as are pressure waves in solids.)

## 1. What is a longitudinal wave?

A longitudinal wave is a type of mechanical wave that causes particles in a medium to vibrate in the same direction as the wave is traveling. This is in contrast to transverse waves, where the particles vibrate perpendicular to the direction of the wave.

## 2. How do longitudinal waves differ from transverse waves?

Longitudinal waves differ from transverse waves in terms of the direction of particle vibration. In longitudinal waves, particles vibrate parallel to the direction of the wave, while in transverse waves, particles vibrate perpendicular to the direction of the wave.

## 3. Are longitudinal waves only found in air?

No, longitudinal waves can travel through any type of medium, including solids, liquids, and gases. However, they are most commonly associated with sound waves traveling through air.

## 4. Can longitudinal waves be reflected?

Yes, longitudinal waves can be reflected when they encounter a boundary between two different mediums. The amount of reflection depends on the properties of the two mediums, such as their density and elasticity.

## 5. How are longitudinal waves used in everyday life?

Longitudinal waves have many practical applications in everyday life, such as in sound technology, medical imaging, and earthquake detection. They are also used in industrial processes, such as ultrasonic testing and cleaning.

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