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?

   • 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
   • Any wave: adding a second wave to the hum can add sound but cannot take sound away
   • Y, whose crests meet the hum's troughs and whose size matches, so the sum is zero
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
   • 0.1 units, since the opposite waves subtract: 1.0 minus 0.9 leaves a small hum
   • 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

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 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
   • Energy is destroyed at seats B and D, where the table shows 0, so the total energy of the room falls

5. Waves on a rope (example data)

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

6. 4.

   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 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 claim holds: the energy rises by 6 units for each extra centimeter of amplitude
7. 5.

   The ripples are 2 cm long. Two dippers make ripples in step. Which points stay calm, Milo?

   • R and S, where the distances differ by the most, 2 cm and 3 cm, so the waves cancel
   • 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
8. 6.

   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?

   • G and I, where the paths differ by 0.4 m and 0.8 m, one and two whole wavelengths
   • F and H, where the paths differ by 0.2 m and 0.6 m, half and one and a half wavelengths
   • F alone, where the two waves travel the most nearly equal distances of any seat
   • H and I, where the paths differ by the most, 0.6 m and 0.8 m, so crests add the most
9. 7.

   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
   • 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 the first note, since 0.25 m is half its wavelength, and loud for the second, since 0.25 m is its whole wavelength

10. Two tuning forks (example data)

    fork	frequency (Hz)
    A	440
    B	444

11. 8.

    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?

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

12. 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

13. 9.

    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 Q, whose frequencies differ by just 1 Hz, so the loudness changes once a second
    • 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
14. 10.

    Zee wants to test whether the quiet spots near two speakers come from interference. Which plan is best?

    • Play different notes through the two speakers, move the speakers apart, and record the loudness at the quietest spot you can find
    • Stand at one spot with both speakers on, listen once, and say the quiet spot shows interference
    • Play one note through both speakers, move a microphone along a line and record loudness, then repeat with one speaker off
    • Record the loudness with both speakers on in this room, then with one speaker on in a different room