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Sound Waves: Frequency, Wavelength and the Wave Equation — Answers

Answer sheet with model answers and success criteria for the 9th Grade energy, light, sound & electricity worksheet.

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Success TutoringWorksheetsAnswer sheet9th Grade · Science · Energy, Light, Sound & Electricity

Sound Waves: Frequency, Wavelength and the Wave Equation — Answers

Part A: What is a sound wave?

Sound is made by vibrating objects. The vibrations push and pull on the air particles, producing compressions (particles squashed together) and rarefactions (particles spread apart) that travel outwards. Because the particles vibrate along the direction the wave travels, sound is a longitudinal wave.

Frequency (in hertz, Hz) decides pitch: higher frequency, higher pitch. Amplitude decides loudness. Humans can hear roughly 20 Hz to 20,000 Hz. Period = 1 ÷ frequency.

1.Match each wave term to its meaning.
  • Amplitude
  • Wavelength (λ)
  • Frequency (f)
  • Period (T)
  • The number of waves passing a point each second, in hertz
  • The time for one complete wave to pass
  • The maximum disturbance from the rest position
  • The distance from one compression to the next

Answer: Amplitude → The maximum disturbance from the rest position; Wavelength (λ) → The distance from one compression to the next; Frequency (f) → The number of waves passing a point each second, in hertz; Period (T) → The time for one complete wave to pass

2.A guitar string is plucked harder, but at the same place. What changes?
  1. AThe pitch gets higher
  2. BThe sound gets louder
  3. CThe sound travels faster
  4. DThe wavelength gets shorter

Answer: The sound gets louder

Plucking harder increases the amplitude, which makes the sound louder. The frequency (pitch) stays the same.

3.Sound waves are transverse waves, like waves on a rope.

Answer: False

Sound waves are longitudinal: the air particles vibrate backwards and forwards in the same direction as the wave travels.

4.Astronauts on a spacewalk cannot talk to each other directly and must use radios. Explain why.

Answer: Sound needs particles (a medium) to travel through. Space is almost a vacuum, so there are no particles to pass on the vibrations. Radio waves are electromagnetic waves, which can travel through a vacuum.

5.A sound has a frequency of 50 Hz. What is its period?

Answer: 0.02 s

  1. T = 1 ÷ f
  2. 1 ÷ 50 = 0.02 s

Part B: The wave equation

Wave speed = frequency × wavelength, or v = fλ, with v in m/s, f in Hz and λ in m. Rearranged: f = v ÷ λ and λ = v ÷ f.

Use 340 m/s for the speed of sound in air.

6.A tuning fork produces a note of 680 Hz in air. What is its wavelength?

Answer: 0.5 m

  1. λ = v ÷ f
  2. 340 ÷ 680 = 0.5 m
7.A sound in air has a wavelength of 1.7 m. What is its frequency?

Answer: 200 Hz

  1. f = v ÷ λ
  2. 340 ÷ 1.7 = 200 Hz
8.Calculate the wavelengths of the lowest (20 Hz) and highest (20,000 Hz) sounds humans can hear.

Answer: 17 m and 0.017 m (1.7 cm)

  1. 20 Hz: 340 ÷ 20 = 17 m
  2. 20,000 Hz: 340 ÷ 20,000 = 0.017 m (1.7 cm)
9.If the frequency of a sound in air is doubled, what happens to its wavelength? Explain using v = fλ.

Answer: The wavelength halves. The speed of sound in air stays the same, so if f doubles, λ must halve to keep f × λ constant.

Part C: Echoes and sonar

An echo is a reflected sound. When using an echo to measure distance, remember the sound travels to the object and back, so divide the total distance by 2.

10.A student claps in front of a large cliff and hears the echo 2.0 s later. How far away is the cliff?

Answer: 340 m

  1. Total distance = speed × time = 340 × 2.0 = 680 m
  2. The sound goes there and back, so distance to cliff = 680 ÷ 2 = 340 m
11.A ship's sonar sends a pulse to the sea floor and receives the echo 0.8 s later. Sound travels at 1500 m/s in sea water. How deep is the water?

Answer: 600 m

  1. Total distance = 1500 × 0.8 = 1200 m
  2. Depth = 1200 ÷ 2 = 600 m
12.You see a flash of lightning and hear the thunder 3 s later. Roughly how far away was the lightning?

Answer: About 1020 m (about 1 km)

  1. Light arrives almost instantly
  2. Distance = 340 × 3 = 1020 m, about 1 km
13.In which material does sound travel fastest?
  1. AAir
  2. BWater
  3. CSteel
  4. DA vacuum

Answer: Steel

Sound travels fastest in solids such as steel (about 5000 m/s), slower in liquids (about 1500 m/s), slower still in gases (about 340 m/s) and not at all in a vacuum.

14.Ultrasound is sound with a frequency above 20,000 Hz. Give one use of ultrasound.

Answer: Any one of: imaging an unborn baby or internal organs; sonar and echo sounding to find depth or fish; cleaning delicate objects; detecting cracks in metal; animals such as bats and dolphins use it to find food (echolocation).

Part D: Explain

15.Explain, using the particle model, why sound travels faster in water than in air, and why it cannot travel through a vacuum. Then explain why a bat can locate a small insect in the dark.[4 marks]

Model answer: Sound is passed on by particles colliding with their neighbors. In water the particles are much closer together than in air, so each vibration is passed on to the next particle more quickly, and the sound travels faster. In a vacuum there are no particles, so the vibrations cannot be passed on at all. A bat sends out high-frequency ultrasound pulses. They reflect off the insect, and the bat detects the echoes. From the time taken for an echo to return, it can judge how far away the insect is, and from the direction of the echo it can tell where the insect is. High-frequency sound has a short wavelength, so it reflects well from small objects.

Success criteria:

  • Sound passed on by particle collisions; closer particles pass vibrations faster
  • No particles in a vacuum, so no sound
  • Bat emits ultrasound and detects reflected echoes
  • Time of echo gives distance (short wavelength suits small objects)
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