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11.9 Waves  (Page 2/7)

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v w = λ T size 12{v size 8{w}= { {λ} over {T} } } {}

or

v w = fλ . size 12{v size 8{w}=fλ} {}

This fundamental relationship holds for all types of waves. For water waves, v w size 12{v rSub { size 8{w} } } {} is the speed of a surface wave; for sound, v w size 12{v rSub { size 8{w} } } {} is the speed of sound; and for visible light, v w size 12{v rSub { size 8{w} } } {} is the speed of light, for example.

Take-home experiment: waves in a bowl

Fill a large bowl or basin with water and wait for the water to settle so there are no ripples. Gently drop a cork into the middle of the bowl. Estimate the wavelength and period of oscillation of the water wave that propagates away from the cork. Remove the cork from the bowl and wait for the water to settle again. Gently drop the cork at a height that is different from the first drop. Does the wavelength depend upon how high above the water the cork is dropped?

Calculate the velocity of wave propagation: gull in the ocean

Calculate the wave velocity of the ocean wave in [link] if the distance between wave crests is 10.0 m and the time for a sea gull to bob up and down is 5.00 s.

Strategy

We are asked to find v w size 12{v rSub { size 8{w} } } {} . The given information tells us that λ = 10 . 0 m size 12{λ="10" "." 0`"m"} {} and T = 5 . 00 s size 12{T=5 "." "00"`"s"} {} . Therefore, we can use v w = λ T size 12{v size 8{w}= { {λ} over {T} } } {} to find the wave velocity.

Solution

  1. Enter the known values into v w = λ T size 12{v size 8{w}= { {λ} over {T} } } {} :
    v w = 10.0 m 5 .00 s . size 12{v size 8{w}= { {"10" "." 0" m"} over {5 "." "00"" s"} } } {}
  2. Solve for v w size 12{v rSub { size 8{w} } } {} to find v w = 2.00 m/s. size 12{v rSub { size 8{w} } } {}

Discussion

This slow speed seems reasonable for an ocean wave. Note that the wave moves to the right in the figure at this speed, not the varying speed at which the sea gull moves up and down.

Transverse and longitudinal waves

A simple wave consists of a periodic disturbance that propagates from one place to another. The wave in [link] propagates in the horizontal direction while the surface is disturbed in the vertical direction. Such a wave is called a transverse wave    or shear wave; in such a wave, the disturbance is perpendicular to the direction of propagation. In contrast, in a longitudinal wave    or compressional wave, the disturbance is parallel to the direction of propagation. [link] shows an example of a longitudinal wave. The size of the disturbance is its amplitude X and is completely independent of the speed of propagation v w size 12{v rSub { size 8{w} } } {} .

The figure shows a woman holding a long spring in her hand and moving it up and down causing it to move in a zigzag manner away from her. It is an example of a transverse wave, the wave propagates horizontally. The direction of motion of the wave is shown with the help of right arrows at each crest and trough.
In this example of a transverse wave, the wave propagates horizontally, and the disturbance in the cord is in the vertical direction.
The figure shows a woman standing at left pushing a long spring in to and fro motion in horizontal direction away from her without moving her hand up and down. The cord stretches and contracts back and forth. This is an example of a longitudinal wave, the wave propagates horizontally. At some points the spring is compressed and at some other points the spring is expanded. One contracted part is equal to the amplitude X.
In this example of a longitudinal wave, the wave propagates horizontally, and the disturbance in the cord is also in the horizontal direction.

Waves may be transverse, longitudinal, or a combination of the two . (Water waves are actually a combination of transverse and longitudinal. The simplified water wave illustrated in [link] shows no longitudinal motion of the bird.) The waves on the strings of musical instruments are transverse—so are electromagnetic waves, such as visible light.

Sound waves in air and water are longitudinal. Their disturbances are periodic variations in pressure that are transmitted in fluids. Fluids do not have appreciable shear strength, and thus the sound waves in them must be longitudinal or compressional. Sound in solids can be both longitudinal and transverse.

The figure shows a guitar connected to an amplifier and a man holding a sheet of paper facing the speaker attached to the amplifier. The strings of the guitar when played cause transverse waves. On the other hand, the sound of the guitar creates ripples on the sheet of paper causing it to rattle in a direction that shows that the sound waves are longitudinal.
The wave on a guitar string is transverse. The sound wave rattles a sheet of paper in a direction that shows the sound wave is longitudinal.
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Source:  OpenStax, College mechanics. OpenStax CNX. Dec 29, 2012 Download for free at http://legacy.cnx.org/content/col11477/1.1
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