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?

   • 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
   • 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
2. 2.

   The copy has the same size as the hum. A headphone adds a copy of the hum, delayed. Which delay cancels the hum, Esme?

   • P, since a copy with no delay reaches the ear first and removes the hum
   • R, since a delay of 1.5 periods puts the copy's crests on the hum's troughs
   • Q, since a delay of 1 period lines the copy's crests up with the hum's crests to cancel them
   • S, since the longest delay gives the copy the most time to cancel the 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 moved, not destroyed: the seats average 2, the same as two speakers give separately, 1 + 1
   • Energy is unchanged at each seat, since a single speaker gives 1 at each seat of 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 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 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
   • The claim holds: any trough cancels a crest, so nothing is left where they meet
   • The claim fails: 3 + (−2) = 1 cm, so a 1 cm crest is left where they meet

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 fails: the energy stays at 2 units no matter how tall the wave becomes
   • 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
9. 6.

   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
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?

    • 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
    • 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

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?

    • 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
    • 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

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 P, because it has the lowest frequencies, which makes the slowest rise and fall in loudness
    • 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