Waves Measurements

Guided Notes Please write out each Comprehension Check question along with any diagrams. Attempt to answer each question using the information presented and your prior knowledge. Be sure to also include definitions and examples in your notes.

The wavelength (λ – Greek letter lambda) in a transverse wave is the distance between two adjacent crests or two adjacent troughs or any two similar adjacent points. Since λ is measuring length, we use the same units as any other length – meters. Comprehension Check: Draw this wave and label 3 examples of ways to measure wavelength.

Comprehension Check: What is the wavelength of this particular wave Comprehension Check: What is the wavelength of this particular wave? Hint – divide the total length by the number of waves in that span. Comprehension Check: How many waves are shown in each harmonic?

In a longitudinal wave, particles of matter vibrate back and forth in the same direction that the wave travels. The wavelength in a longitudinal wave is the distance between the center of two adjacent compressions. Since λ is measuring length, we use the same units as any other length – meters. Comprehension Check: Draw this wave and label the wavelength.

Wavelength Animations

The period, (T ), is the amount of time for the harmonic motion to repeat itself, or for the object to go one full cycle. In simple harmonic motion, T is the time it takes the object to return to its exact starting point and starting direction. The period of a wave depends on the period of oscillation of the object creating the wave. T is usually measured in seconds. Comprehension Check: What is the magnitude of the period of this wave?

The number of waves that pass a fixed point in a given amount of time is wave frequency (f). Wave frequency can be measured by counting the number of waves that pass the fixed point in 1 second or some other time period. The higher the number is, the greater the frequency of the waves. The SI unit for wave frequency is the hertz (Hz), where 1 hertz equals 1 wave passing a fixed point in 1 second. Comprehension Check: How is frequency related to wavelength?

Comprehension Check: What is the frequency of this wave?

Check out some transverse waves with different frequencies: https://phet.colorado.edu/en/simulation/wave-on-a-string Wave on a String

Wave amplitude (a) is the maximum distance the particles of the medium move from their equilibrium position when a wave passes through. The resting position of a particle of the medium is where the particle would be in the absence of a wave. Waves with greater amplitude are transferring greater energy. Comprehension Check: Label two more instances of amplitude on this graph.

Comprehension Check: Does this picture infer that wave amplitude correlates with volume or pitch?

In a longitudinal wave, particles of the medium move back and forth in the same direction as the wave. Wave amplitude of a longitudinal wave is related to the density of particles of the medium where it is compressed by the wave. The closer together (more dense) the particles are, the greater the amplitude of the wave. Comprehension Check: Which of the sound waves above would have the greater amplitude and thus be carrying the most energy?

The frequency of a wave is the same as the frequency of the vibrations that caused the wave. For example, to generate a higher frequency wave in a rope, you must move the rope up and down more quickly. This takes more energy, so a higher frequency wave has more energy than a lower-frequency wave with the same amplitude. Comprehension Check: Is Tommy Turtle or Ricky Rabbit giving more energy to his wave? What is the same about both waves?

Wave speed depends on the medium through which the wave travels. Density of materials – how many molecules there are to bump into each other Elasticity – how well it changes shape and then springs back. More elastic = faster waves Temperature – the higher the temperature the faster the molecules move Comprehension Check: What 3 factors affect wave speed? Would you hear firecrackers popping (from 1 km away) faster on New Year’s Day or on Independence Day?

Sound travels about 330 m/s to 350 m/s depending   Sound travels about 330 m/s to 350 m/s depending on the temperature of the air. It travels 4 times faster in water, and 15 times faster in steel. Wave Speed = frequency x wavelength v = λf

Sound waves at a concert reach your ears at the Frequency (Hz) Wavelength (m) Wave Speed (m/s) 160 2.13 340 264 1.29 340 396 0.86 340 528 0.64 340 Sound waves at a concert reach your ears at the same time. Lower notes have long waves, high notes (higher frequency) have shorter wave lengths, but they all have the same wave speed.

Comprehension Check: What is the wavelength of a 340 Hz sound wave when the speed of sound in air is 340 m/s? Wavelength = speed = 340 m/sec = 1 meter/cycle Frequency 340 cycles/sec 1 miles = 1609 meters. If the speed of sound is 340 m/s, how long does it take for thunder to travel 1 mile? T = distance/speed 1609 m = 4.7 seconds 340 m/sec So about 5 seconds/mile

Frequency = 1/period (T) Period = 1/frequency (f) f = 1/T T = 1/f If a wave’s frequency is known, then you can calculate the period of time it takes for one wave to pass. Frequency = 1/period (T) Period = 1/frequency (f) f = 1/T T = 1/f It is an inverse relationship Comprehension Check: If the frequency of a wave is 2 Hz, what is its period? If the period of a wave is 5 seconds, what is its frequency? T = 1/f = ½ = 0.5 s f = 1/T = 1/5 = 0.2 Hz

The sears building in Chicago sways back and forth at a vibration of 0 The sears building in Chicago sways back and forth at a vibration of 0.1 Hz. What is its Period of Vibration? T = 1/f T = 1/0.1 cycles/sec = 10 seconds/cycle It takes 10 seconds for it to sway back and forth one time

Comprehension Check – Sample Problems Make sure to begin each one with the appropriate equation and show your work. Calculate the frequency of a sound wave when its speed is 350 m/s and its wavelength is 0.175 m. Calculate the period of a wave when f = 25 Hz f = v/λ = 350/0.175 = 2000 Hz T = 1/f = 1/25 = 0.04 seconds

Comprehension Check – Sample Problems Make sure to begin each one with the appropriate equation and show your work. A sound wave travels at 343 m/s and a compression passes by every 0.12 seconds. Determine the frequency of this wave. Determine the wavelength of a gamma wave when its speed is 3 x 108 and its frequency is 4 x 1017 Hz. If a compression passes by every 0.12 seconds that means the period for this wave is 0.12 seconds. (Period is T) f = 1/T = 1/0.12 = 8.3 Hz λ=v/f = 3 x 108 / 4 x 1017 = 0.75 x 10-9 = 7.5 x 10-10