Waves that add and cancel

Grade 8 Science Worksheet - Challenge Me

Circle the best answer.

1. 1.

   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?

   • Y, whose crests meet the hum's troughs and whose size matches, so the sum is zero
   • Z, whose crests meet the hum's troughs, which cancels any hum whatever the wave's size
   • Any wave: adding a second wave to the hum can add sound but cannot take sound away
   • X, whose crests match the hum's crests and whose size matches, so the two waves agree
2. 2.

   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
   • 1.9 units, since the two amplitudes add whenever two waves meet at one spot
   • 0.1 units, since the opposite waves subtract: 1.0 minus 0.9 leaves a small hum

3. 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

4. 3.

   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

5. A crest and a trough meeting on a rope (example data)

   wave	height at the meeting point (cm)
   Crest	3
   Trough	−2

6. 4.

   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: the 1 cm that is left is too small to count as a wave
   • The claim holds: any trough cancels a crest, so nothing is left where they meet
   • The claim fails: the 2 cm trough has no effect, so the full 3 cm crest stays

7. Waves on a rope (example data)

   amplitude (cm)	energy carried each second (units)
   1	2
   2	8
   3	18

8. 5.

   Luz says a combined wave with twice the amplitude carries twice the energy. What does the table show?

   • The claim holds: the energy rises by 6 units for each extra centimeter of amplitude
   • The claim fails: doubling the amplitude from 1 cm to 2 cm took the energy from 2 to 8, four times
   • The claim holds: a taller wave is a stretched copy, so doubling the amplitude doubles the energy it carries
   • The claim fails: the energy stays at 2 units no matter how tall the wave becomes
9. 6.

   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
   • R and S, where the distances differ by the most, 2 cm and 3 cm, so the waves cancel
   • Q alone, where the distances differ by exactly half a wavelength, and no other point
   • P and R, where the distances differ by no wavelengths and by one whole wavelength
10. 7.

    The note has a wavelength of 0.4 m. Room echoes are ignored. Two speakers play one note in step. At which seats is the sound loudest, Noah?

    • F alone, where the two waves travel the most nearly equal distances of any seat
    • G and I, where the paths differ by 0.4 m and 0.8 m, one and two whole wavelengths
    • H and I, where the paths differ by the most, 0.6 m and 0.8 m, so crests add the most
    • F and H, where the paths differ by 0.2 m and 0.6 m, half and one and a half wavelengths
11. 8.

    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 the first note, since 0.25 m is half its wavelength, and quiet for the second, since 0.25 m is its whole wavelength
    • 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 both notes, since the speakers play in step and the seat is almost the same distance from both

12. Two tuning forks (example data)

    fork	frequency (Hz)
    A	440
    B	444

13. 9.

    Ren sounds two tuning forks together, and the sound gets louder and softer again and again. How many times each second does it get loud?

    • 4 times each second, the difference between 444 Hz and 440 Hz
    • 2 times each second, half of the difference between the two frequencies
    • 442 times each second, the average of the two frequencies of the forks
    • 884 times each second, the sum of the two frequencies, 444 Hz and 440 Hz

14. 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

15. 10.

    Two forks sound together in each pair. Which pair makes the loudness rise and fall most slowly, Tala?

    • Pair R, because its frequencies add up to the largest total, which slows the changes
    • Pair P, because it has the lowest frequencies, which makes the slowest rise and fall in loudness
    • Pair Q, whose frequencies differ by just 1 Hz, so the loudness changes once a second
    • Pair S, because a gap of 2 Hz is a middle value, which gives a steady, slow change