Waves that add and cancel
Grade 8 Science Worksheet - Challenge Me
Circle the best answer.
Each wave repeats every 4 ms. Headphones add an anti-noise wave to cancel a hum. Which wave in the table leaves the quietest sound, Ari?
- Any wave: adding a second wave to the hum can add sound but cannot take sound away
- Z, whose crests meet the hum's troughs, which cancels any hum whatever the wave's size
- X, whose crests match the hum's crests and whose size matches, so the two waves agree
- Y, whose crests meet the hum's troughs and whose size matches, so the sum is zero
Each wave repeats every 4 ms. The anti-noise wave is slightly too small. What is the hum's amplitude after the two waves are added, Bo?
- 0.9 units, since the anti-noise wave replaces the hum that was there before
- 0 units, since waves whose crests meet troughs cancel completely, whatever their sizes
- 0.1 units, since the opposite waves subtract: 1.0 minus 0.9 leaves a small hum
- 1.9 units, since the two amplitudes add whenever two waves meet at one spot
The copy has the same size as the hum. A headphone adds a copy of the hum, delayed. Which delay cancels the hum, Esme?
- S, since the longest delay gives the copy the most time to cancel the hum
- P, since a copy with no delay reaches the ear first and removes the hum
- Q, since a delay of 1 period lines the copy's crests up with the hum's crests to cancel them
- R, since a delay of 1.5 periods puts the copy's crests on the hum's troughs
Read this first
Sound intensity at four seats (example data)
seat one speaker alone both speakers A 1 4 B 1 0 C 1 4 D 1 0 Jun says destructive interference destroys sound energy. Which statement fits the table?
- Energy is destroyed at seats B and D, where the table shows 0, so the total energy of the room falls
- Energy is unchanged at each seat, since a single speaker gives 1 at each seat of the table
- Energy is moved, not destroyed: the seats average 2, the same as two speakers give separately, 1 + 1
- Energy is created at seats A and C, where 4 is more than 1, so the total energy of the room rises
A crest and a trough meeting on a rope (example data)
wave height at the meeting point (cm) Crest 3 Trough −2 Kira says a 2 cm trough cancels a 3 cm crest completely where they meet. What does the table show?
- The claim fails: 3 + (−2) = 1 cm, so a 1 cm crest is left where they meet
- The claim holds: any trough cancels a crest, so nothing is left where they meet
- The claim holds: the 1 cm that is left is too small to count as a wave
- The claim fails: the 2 cm trough has no effect, so the full 3 cm crest stays
Waves on a rope (example data)
amplitude (cm) energy carried each second (units) 1 2 2 8 3 18 Luz says a combined wave with twice the amplitude carries twice the energy. What does the table show?
- The claim holds: a taller wave is a stretched copy, so doubling the amplitude doubles the energy it carries
- The claim holds: the energy rises by 6 units for each extra centimeter of amplitude
- The claim fails: the energy stays at 2 units no matter how tall the wave becomes
- The claim fails: doubling the amplitude from 1 cm to 2 cm took the energy from 2 to 8, four times
The ripples are 2 cm long. Two dippers make ripples in step. Which points stay calm, Milo?
- Q and S, where the distances differ by half and by one and a half wavelengths
- P and R, where the distances differ by no wavelengths and by one whole wavelength
- Q alone, where the distances differ by exactly half a wavelength, and no other point
- R and S, where the distances differ by the most, 2 cm and 3 cm, so the waves cancel
Sound travels 343 m/s in air, so frequency times wavelength is 343. Speakers play each note in step. Seat S is 6.0 m from one speaker and 6.25 m from the other. What does Pia hear at S?
- Loud for both notes, since the speakers play in step and the seat is almost the same distance from both
- Quiet for both notes, since the 0.25 m path difference does not change when the note changes
- Quiet for the first note, since 0.25 m is half its wavelength, and loud for the second, since 0.25 m is its whole wavelength
- Loud for the first note, since 0.25 m is half its wavelength, and quiet for the second, since 0.25 m is its whole wavelength
Four pairs of tuning forks (example data)
pair fork 1 (Hz) fork 2 (Hz) P 256 260 Q 440 441 R 440 445 S 256 258 Two forks sound together in each pair. Which pair makes the loudness rise and fall most slowly, Tala?
- Pair S, because a gap of 2 Hz is a middle value, which gives a steady, slow change
- Pair R, because its frequencies add up to the largest total, which slows the changes
- Pair Q, whose frequencies differ by just 1 Hz, so the loudness changes once a second
- Pair P, because it has the lowest frequencies, which makes the slowest rise and fall in loudness
Zee wants to test whether the quiet spots near two speakers come from interference. Which plan is best?
- Play one note through both speakers, move a microphone along a line and record loudness, then repeat with one speaker off
- Stand at one spot with both speakers on, listen once, and say the quiet spot shows interference
- Play different notes through the two speakers, move the speakers apart, and record the loudness at the quietest spot you can find
- Record the loudness with both speakers on in this room, then with one speaker on in a different room