Wave Properties

Wave Properties

• Wave properties are covered in Week 17, Explore 1 and Explore 2.
• The textbook reference is pages 96-101.

Objectives

• Use the following units: degree (°), hertz (Hz), metre (m), metre/second (m/s), second (s).
• Explain the difference between longitudinal and transverse waves.
• Define amplitude, wavefront, frequency, wavelength, and period of a wave.
• Waves transfer energy and information without transferring matter.
• Know and use the relationship between speed, frequency, and wavelength: wave speed = frequency × wavelength (v = f x λ).
• Use the relationship between frequency and time period: frequency = 1/time period (f = 1/T).

Starter - What is a Wave?

• A wave is the transfer of energy without the transfer of matter.

Describing Waves

• Wavelength is the distance between one point on a disturbance and the same point measured on the next, (m).
• Could be peak to peak distance.
• Amplitude is the maximum displacement from the origin, (m).
• Time period is the time taken for one complete oscillation, (s).
• If frequency is increased there are more waves per second on screen.
• The higher the amplitude, the taller the wave.
• Sound waves are particles either stretching out from each other or bunching together.
• Displacement vs. distance graph of a wave shows the amplitude and wavelength.

Describing waves - Period and Frequency

• Time period of a wave is the time for one complete cycle.
• Frequency is the number of cycles per second.
• Frequency and time are reciprocal of each other.
• T is the time period in seconds and f is the frequency in Hertz.
• The wavelength of a wave is 40cm from a displacement/distance graph.
• The amplitude of a wave is 2m.
• To find the frequency of a wave:
  • Period = T = 10s
  • f = 1/T = (insert calculation)
  • Frequency = T = 0.4s
  • f = 1/t = 1/0.4 = 2.5 Hz

Types of Wave

• Vibrations are perpendicular to energy transfer in a transverse wave.
• Vibrations are parallel in a longitudinal wave.
• Compression is an area of higher pressure where particles are squashed together.
• Rarefaction is an area of low pressure when the particles are stretched apart.

Plenary - Examples of Transverse and Longitudinal

• Light, radio waves, gamma rays, infra-red, (electromagnetic spectrum), water waves, and S waves (secondary seismic waves) are transverse waves.
• Sound, ultrasound, and P waves (primary seismic waves) are longitudinal waves.
• Light waves and water waves are transverse.
• Sound waves are longitudinal.

Starter

• The wavespeed equation is v = fλ.
  • v is velocity in m/s.
  • f is frequency in Hz.
  • λ is wavelength in m.

Converting Units

• 24 kHz = 24000 Hz
• 5.5 kHz = 5500 Hz
• 120 km = 120000 m
• 40 km = 40000 m
• 356 cm = 3.56 m
• 20 mm = 0.02 m
• 136.25 mm = 0.14 m

Exam Questions

• Air horn produces sound waves at frequency of 420 Hz, wavelength 0.80 m.
• The speed of the sound waves is calculated as follows:
  • v = fλ
  • v = 420 × 0.80
  • v = 336 m/s
• Mobile phone network uses microwaves to transmit signal, that frequency of 1.8×10⁹ Hz and travel at a speed of 3×10⁸ m/s. is calculated as follows:
  • v = fλ
  • 3×10⁸ = 1.8×10⁹ χλ
  • λ = 3×10⁸/1.8×10⁹
  • λ = 0.17 m

Answers

• A sound wave steel frequency 500Hz wavelength of 3.0 metres is calculated as follows:
  • v = f x λ
  • v = 500 × 3.0 = 1500 m/s
• Ripple on a pond frequency of 2 Hz wavelength of 0.4 metres is calculated as follows:
  • v = f x λ
  • v = 2 × 0.4 = 0.8 m/s
• Radio wave with wavelength of 30 m frequency of 10,000,000 hertz is calculated as follows:
  • v = f x λ
  • v = 10000000 x 30
  • v = 300000000 m/s or
  • v = f x λ
  • v = 1 x 10⁷ x 30
  • v = 3.0 × 10⁸ m/s

Wave Speed

• Slinky spring frequency of 2 Hz travelling at 3 m/s. is calculated as follows:
  • λ = v/f
  • = 3/2
  • = 1.5 m
• Ultrasound wave frequency 40000 Hz travelling at 1450 m/s in fatty tissue is calculated as follows:
  • λ = v/f
  • λ 1450 / 40000
  • λ = 0.036 m
• Sound wave frequency 440 Hz travelling at 340 metres per second in air is calculated as follows:
  • λ = v/f
  • λ = 340/440
  • λ = 0.773 m

Wave Frequency

• Sound wave wavelength 10 metres travelling at 340 metres per second in air is calculated as follows:
  • f = v / λ
  • f = 340/10
  • f = 34 Hz
• The wave on the sea with a speed of 8 m/s and a wavelength of 20 metres. is calculated as follows:
  • f = v / λ
  • f = 8/20
  • f = 0.4 Hz
• The Microwave wavelength 0.15 metres travelling through space at 300,000,000 m/s. is calculated as follows:
  • f = v / λ
  • f = 300000000 / 0.15
  • f = 2000000000 Hz or
  • f = v / λ
  • f = 3.0 x 108 / 0.15
  • f = 2.0 × 10º Hz