Educational worksheet on wave types and properties for science learning.

Let’s go step by step to fill in the blanks using the word bank and then label the diagrams.

We’ll use these words from the Word Bank:
- Longitudinal
- amplitude
- transverse
- sound
- wavelength
- peaks
- frequency
- hertz
- energy
- troughs

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Sentence 1:
“E______ travels in waves.”
→ Waves carry energy. So, answer: Energy

Sentence 2:
“Transverse waves move up and down in patterns that have high points called ______ a ______.”
→ High points are called peaks. The sentence says “called ___ a ___” — probably meant to be “called peaks”. But looking at structure: maybe it’s “called _p_ e _a_ k_s_”? Wait — actually, re-reading: “have high points called ______ a ______.” That seems like a typo or formatting issue. Probably should be “called peaks”. But let’s check the blank pattern: “_ _ _ _ _ a _ _ _ _” — no, wait, original says: “called ______ a ______.” Hmm. Maybe it’s “called crests and troughs”? No — transverse waves have peaks (crests) and troughs. But the sentence says “high points”, so only peaks. Perhaps it’s “called peaks” and the “a” is part of the word? Let me look again.

Actually, looking at the original text:
“2. Transverse waves move up and down in patterns that have high points called ______ a ______.”

Wait — perhaps it’s “called _c_r_e_s_t_s_”? But “crests” isn’t in the word bank. Word bank has “peaks”. And “peaks” fits. Also, later it mentions “troughs” for low points. So likely, this is “called peaks” — but why “a”? Maybe it’s a misprint. Alternatively, maybe it’s “called peaks and troughs” — but that would be two things. Sentence says “high points”, plural, so “peaks”. I think we should put “peaks” here. But the blank is split: “______ a ______” — maybe it’s “peaks” as one word? Or perhaps it’s “crest” but not in bank. Let’s skip and come back.

Actually, looking at standard science terms: transverse waves have crests (high) and troughs (low). But “crests” isn’t in the word bank — “peaks” is. So they’re using “peaks” for crests. So sentence 2: “high points called peaks” — but the blank is written as “______ a ______” — maybe it’s a typo and should be just one blank? Or perhaps it’s “called _p_e_a_k_s_” — but that doesn’t fit “a”. Another idea: maybe it’s “called _w_a_v_e_s_”? No. Let’s read carefully: “have high points called ______ a ______.” Perhaps it’s “called peaks” and the “a” is a mistake. Or maybe it’s “called crests” — but not in bank. I think we should go with “peaks” and assume the “a” is part of the word or a formatting error. Actually, looking at the image description, it might be “called _c_r_e_s_t_s_” but since “crests” isn’t in bank, and “peaks” is, and sentence 3 mentions “troughs”, I think sentence 2 is “peaks”.

But let’s check sentence 3: “The low points of a transverse wave are called _t_r_o_u_g_h_s_.” Yes! So sentence 2 must be “peaks”. So for sentence 2: “called peaks” — but the blank is “______ a ______” — perhaps it’s “peaks” as one word, and the “a” is a separator? Maybe it’s “called _p_e_a_k_s_” — but that’s 5 letters. I think we should write “peaks” for the first blank and ignore the “a” or consider it part of the word. Alternatively, maybe it’s “called crest and trough” — but again, not matching. Let’s proceed with “peaks” for sentence 2.

Actually, upon second thought, the sentence says: “have high points called ______ a ______.” This might be a typo, and it should be “called peaks” — so perhaps the “a” is meant to be part of “peaks”? Unlikely. Another possibility: in some contexts, people say “peaks and valleys”, but “valleys” isn’t in bank. I think the best fit is “peaks” for the high points. So I’ll put “peaks” in the first blank and leave the second? No, that doesn’t work. Let’s look at the word bank again. Words: Longitudinal, amplitude, transverse, sound, wavelength, peaks, frequency, hertz, energy, troughs.

Perhaps sentence 2 is: “called _p_e_a_k_s_” — but the blank is split. Maybe it’s “called crests” — but not in bank. I recall that in some curricula, they use “peaks” for crests. So I’ll assume sentence 2 is “peaks” and the “a” is a mistake. Or perhaps it’s “called _w_a_v_e_ p_e_a_k_s_”? Too long. Let’s move to sentence 3 and come back.

Sentence 3:
“The low points of a transverse wave are called _t_r_o_u_g_h_s_.”
→ From word bank: troughs — perfect match. So answer: troughs

Now, sentence 2: if low points are troughs, high points are peaks. So sentence 2 should be “peaks”. The “a” might be a typo. Perhaps it’s “called peaks” and the blank is for “peaks”. I’ll go with peaks for sentence 2.

Sentence 4:
“The distance between any two troughs or peaks is called the _w_a_v_e_l_e_n_g_t_h_.”
→ That’s wavelength. Answer: wavelength

Sentence 5:
“The height of a peak or trough is called the _a_m_p_l_i_t_u_d_e_.”
→ amplitude. Answer: amplitude

Sentence 6:
“_F_r_e_q_u_e_n_c_y_ is the number of complete waves that pass by in one second.”
→ frequency. Answer: frequency

Sentence 7:
“Frequency is measured in _h_e_r_t_z_ (which is written Hz).”
→ hertz. Answer: hertz

Sentence 8:
“_L_o_n_g_i_t_u_d_i_n_a_l_ waves move by pushing forward and pulling back.”
→ Longitudinal. Answer: Longitudinal

Sentence 9:
“_S_o_u_n_d_ waves are examples of longitudinal waves.”
→ sound. Answer: sound

Sentence 10:
“Waves on the surface of water are examples of _t_r_a_n_s_v_e_r_s_e_ waves.”
→ Water surface waves are transverse (though technically a mix, but in basic science, taught as transverse). Answer: transverse

Now, back to sentence 2: “Transverse waves move up and down in patterns that have high points called ______ a ______.”

Given that sentence 3 is “troughs”, and word bank has “peaks”, I think it’s safe to say sentence 2 is “peaks”. The “a” might be a formatting error, or perhaps it’s “called peaks” and the blank is for “peaks”. Maybe it’s “called _c_r_e_s_t_s_” but not in bank. I’ll go with peaks for the first part, and since there’s an “a”, perhaps it’s “peaks” as one word. Or maybe it’s “called crest and trough” — but that doesn’t fit. Another idea: perhaps it’s “called _w_a_v_e_ p_e_a_k_s_” — no. I think the intended answer is “peaks”, so I’ll put peaks in the blank, ignoring the “a” as a typo.

Actually, looking at the original text: “called ______ a ______.” — perhaps it’s “called _p_e_a_k_s_” and the “a” is part of the word? Like “peaks” has ‘a’ in it? No. Maybe it’s “called crests” — but not in bank. I found a better way: in some texts, they say “high points called crests”, but since “crests” isn’t in bank, and “peaks” is, and it’s commonly used interchangeably in elementary levels, I’ll use peaks.

So for sentence 2: peaks

Now, labeling the diagrams.

First diagram: Wave with labels a, b, c, d, e.

From the sketch:

- a: looks like the highest point → peak or crest
- b: vertical line from rest position to peak → amplitude
- c: horizontal line showing one full cycle → wavelength
- d: lowest point → trough
- e: the resting position line → but usually not labeled, or sometimes "equilibrium". But in the context, e might be the wavelength indicator? Wait, in the diagram, e is under the wave, probably indicating the length of one wave. Looking at standard labeling:

Typically:
- a: crest (peak)
- b: amplitude (height from rest to crest)
- c: wavelength (distance between two crests or troughs)
- d: trough
- e: might be the same as c, or perhaps the period, but in this case, since it's a spatial diagram, e is likely another way to show wavelength, but usually c is wavelength. In the diagram, c is marked from crest to crest, so c is wavelength. e is marked from start to end of one wave, so also wavelength? But that would be redundant. Perhaps e is the wave itself or something else. Let's think.

In many diagrams:
- a: crest
- b: amplitude
- c: wavelength
- d: trough
- e: could be the equilibrium position, but it's labeled below the wave. In the user's description, it says "e." under the wave, and it's a horizontal line spanning one wave, so likely wavelength again? But that doesn't make sense. Perhaps e is the direction of wave travel or something. But in standard terms, for a transverse wave diagram:

Common labels:
- Peak/crest: a
- Amplitude: b (vertical arrow)
- Wavelength: c (horizontal arrow from crest to crest)
- Trough: d
- e: might be the baseline or rest position, but it's labeled as "e." and it's a line under the wave. In some diagrams, e is used for the wavelength measurement. But c is already wavelength. Perhaps c is from peak to peak, and e is from trough to trough, but both are wavelength. I think e is also indicating wavelength, but that's duplicate. Maybe e is the period, but period is time, not space. Since this is a snapshot, all are spatial.

Looking back at the problem: "label each diagram" — and there are two diagrams: one transverse (with a,b,c,d,e) and one longitudinal (f).

For the transverse wave diagram:
- a: peak (or crest)
- b: amplitude
- c: wavelength
- d: trough
- e: ? In many textbooks, e might be the equilibrium position, but it's drawn as a line under the wave. Perhaps e is the wave speed or something, but unlikely. Another possibility: e is the distance for one wavelength, same as c. But that would be odd. Perhaps in this diagram, c is from peak to peak, and e is from start to end of the wave shown, which is one wavelength. So both c and e represent wavelength? But that doesn't help. Let's see the word bank: we have to use words from bank. Words left: after filling sentences, we have used: energy, peaks, troughs, wavelength, amplitude, frequency, hertz, Longitudinal, sound, transverse. All words are used in sentences, but for labeling, we need to assign terms.

Perhaps for the diagram, we use the same terms.

Standard labeling for transverse wave:
- a: crest (but "crest" not in bank, so "peak")
- b: amplitude
- c: wavelength
- d: trough
- e: could be the rest position, but "rest position" not in bank. Or perhaps e is not labeled with a term from bank, but the instruction is to label using the concepts.

Another idea: in some diagrams, e is the direction of propagation, but not specified. Perhaps e is the wave itself, but that's vague. Let's look at the longitudinal wave diagram f.

Diagram f: shows compressions and rarefactions. For longitudinal waves, we label:
- Compressions (where coils are close)
- Rarefactions (where coils are spread)
- Wavelength (distance between two compressions)

But the word bank has "Longitudinal", "sound", etc., but for labeling, we need specific parts.

Perhaps for diagram f, we label the compressions and rarefactions, but those terms aren't in the word bank. Word bank has "Longitudinal", which is the type, but for parts, we might use "wavelength" or "amplitude", but amplitude in longitudinal is different.

This is tricky. Let's rethink.

Perhaps for the transverse wave diagram:
- a: peak
- b: amplitude
- c: wavelength
- d: trough
- e: ? Maybe e is the equilibrium line, but not in bank. Or perhaps e is the frequency, but frequency is not spatial. I think e might be intended to be the wavelength again, but that's redundant. Another possibility: in some diagrams, e is used for the period, but again, not spatial.

Let's count the blanks in sentences: we have 10 sentences, and we filled them with 10 words from bank. For the diagrams, we need to label a,b,c,d,e,f with appropriate terms, possibly from the same concepts.

For diagram f (longitudinal wave), typically:
- The regions where particles are close together are compressions.
- Where they are far apart are rarefactions.
- The wavelength is the distance between two consecutive compressions.

But "compression" and "rarefaction" are not in the word bank. Word bank has "Longitudinal", "sound", etc. Perhaps for f, we label it as "Longitudinal wave", but it's already implied.

The instruction is: "Then label each diagram." and the diagrams have letters a to f.

For the transverse wave:
- a: the high point → peak
- b: the vertical distance from rest to peak → amplitude
- c: the horizontal distance from one peak to next → wavelength
- d: the low point → trough
- e: in the diagram, e is likely the same as c, or perhaps the baseline. But in many worksheets, e is used for the wavelength measurement along the bottom. So perhaps e is also wavelength, but that's duplicate. Maybe e is the wave speed, but not in bank.

Perhaps e is the "rest position" or "equilibrium", but not in bank. Let's see the word bank again: all words are used in sentences, so for labeling, we might reuse terms.

Another idea: for e, it might be the "frequency", but frequency is not a spatial feature. I think there's a mistake in my approach.

Let's list what we have for sentences:

1. Energy
2. peaks (assuming)
3. troughs
4. wavelength
5. amplitude
6. frequency
7. hertz
8. Longitudinal
9. sound
10. transverse

All 10 words used.

For the diagrams, we need to label a,b,c,d,e,f with terms like peak, trough, amplitude, wavelength, etc., even if not in the sentence blanks.

For transverse wave diagram:
- a: peak
- b: amplitude
- c: wavelength
- d: trough
- e: ? In the diagram, e is probably the length of one wave, so wavelength, but c is already that. Perhaps e is the direction or something else. Maybe e is the "wave" itself, but not helpful. In some diagrams, e is used for the period, but again, not spatial. Perhaps e is not to be labeled with a term from bank, but the instruction is to label.

Let's look at the longitudinal wave diagram f. It shows a spring with compressions. Typically, for such a diagram, we might label:
- A compression
- A rarefaction
- Wavelength

But since "compression" and "rarefaction" aren't in bank, perhaps we label f as "Longitudinal" or "sound", but that's the type, not a part.

Perhaps for f, we label the wavelength or amplitude.

I recall that in longitudinal waves, the amplitude is related to how much the particles are displaced, but it's not easy to label on a spring diagram.

Another thought: in the transverse wave diagram, e might be the "equilibrium position", but not in bank. Perhaps e is the "baseline" or "rest line".

But let's check online or standard practice. Upon recalling, in many school worksheets, for a transverse wave diagram:
- a: crest
- b: amplitude
- c: wavelength
- d: trough
- e: often the same as c, or sometimes the wave number, but usually, e is not used, or it's the direction.

Perhaps in this case, e is the distance for one wavelength, so wavelength, and c is also wavelength, but that's fine.

For diagram f, the longitudinal wave, we can label:
- f: the type of wave, but it's already "Wave" above, so perhaps label the parts. But the letter f is next to the diagram, so likely f is to be labeled as "Longitudinal" or something.

The diagram is labeled "f. ______ Wave", so for f, we need to fill in the type. From sentence 8 and 9, longitudinal waves are like sound, so f is Longitudinal wave.

Then for the parts inside the diagrams, a,b,c,d,e are to be labeled with terms like peak, amplitude, etc.

So for transverse wave:
- a: peak
- b: amplitude
- c: wavelength
- d: trough
- e: ? What is e? In the diagram, e is a horizontal line under the wave, spanning one full cycle, so it's indicating the wavelength. So e is also wavelength. But that's the same as c. Perhaps c is from peak to peak, and e is from trough to trough, but both are wavelength. Or perhaps e is the period, but not spatial. I think it's safe to say e is wavelength.

But let's see if there's another term. Perhaps e is the "frequency", but frequency is not a length. Another idea: in some contexts, e might be the "speed", but not in bank.

Perhaps e is the "energy", but energy is not a geometric feature.

I think the intended labeling is:
- a: peak
- b: amplitude
- c: wavelength
- d: trough
- e: wavelength (again, or perhaps the wave itself)

But to avoid duplication, maybe e is the "rest position". Let's assume that.

Upon second thought, in the diagram, b is the amplitude (vertical), c is wavelength (horizontal from peak to peak), d is trough, a is peak, and e is likely the baseline or equilibrium line. But "equilibrium" not in bank. Perhaps "rest position", but not in bank.

Word bank has "energy", "hertz", etc., not suitable.

Another possibility: for e, it might be the "period", but period is time, not shown in spatial diagram.

I recall that in some diagrams, e is used for the wave's direction of travel, but not specified.

Perhaps for e, it's not labeled, but the instruction is to label each.

Let's look at the longitudinal wave diagram. It has no internal labels, only f for the type.

So for f, we put "Longitudinal" as the type of wave.

Then for a,b,c,d,e in transverse wave, we use:
- a: peak
- b: amplitude
- c: wavelength
- d: trough
- e: ? Perhaps "frequency", but doesn't fit. Or "hertz", no.

Maybe e is the "sound" wave, but not.

I think there's a mistake. Let's read the user's input: "label each diagram" and the diagrams have a,b,c,d,e for the first, and f for the second.

In the first diagram, e is probably the wavelength indicator, so wavelength.

For the second diagram, f is the type, so Longitudinal.

But "Longitudinal" is already used in sentence 8, but we can reuse for labeling.

Similarly, for a,b,c,d,e, we use the terms.

So let's finalize:

Sentences:
1. Energy
2. peaks (for "high points called peaks")
3. troughs
4. wavelength
5. amplitude
6. frequency
7. hertz
8. Longitudinal
9. sound
10. transverse

Diagrams:
- a: peak
- b: amplitude
- c: wavelength
- d: trough
- e: wavelength (since it's the length of one wave)
- f: Longitudinal (as the type of wave)

But e and c are both wavelength, which is redundant, but possible.

Perhaps e is the "crest" but we have peak. Or in some systems, e is the "node" but not for transverse.

Another common labeling: in some diagrams, e is the distance from start to end, which is wavelength, so ok.

For f, since it's "f. ______ Wave", and from sentence 8, longitudinal waves move by pushing and pulling, and diagram f shows that, so f is Longitudinal.

Also, for the transverse wave, a is peak, d is trough, b is amplitude, c is wavelength, e might be the equilibrium, but since not in bank, perhaps it's not labeled, but the instruction is to label.

Perhaps e is the "frequency", but that doesn't make sense spatially.

I found a better way: in the diagram, e is likely the wavelength, and c is also wavelength, but c is from peak to peak, e is from the beginning to end of the wave shown, which is one wavelength, so same thing.

So I'll go with that.

Now for the final answer, we need to provide the filled sentences and labeled diagrams.

But the user asked to solve the problem, so we need to output the answers.

Since the options are false, we only provide Final Answer.

So let's compile:

Filled sentences:
1. Energy
2. peaks (assuming the "a" is a typo or part of the word)
3. troughs
4. wavelength
5. amplitude
6. frequency
7. hertz
8. Longitudinal
9. sound
10. transverse

Diagram labels:
- a: peak
- b: amplitude
- c: wavelength
- d: trough
- e: wavelength (or perhaps "rest position", but I think wavelength is intended)
- f: Longitudinal

But for e, in some sources, e is the equilibrium line, but since not in bank, and "wavelength" is available, and it's a length, I'll use wavelength.

To confirm, let's see if there's a standard. Upon quick search in memory, in many worksheets, for a transverse wave, the label e is often the wavelength when measured along the bottom.

So ok.

For f, it's "Longitudinal" wave.

Now, for sentence 2, to resolve the "a", perhaps it's "called peaks" and the blank is for "peaks", so we write "peaks".

So final answers:

Sentences:
1. Energy
2. peaks
3. troughs
4. wavelength
5. amplitude
6. frequency
7. hertz
8. Longitudinal
9. sound
10. transverse

Diagram:
a: peak
b: amplitude
c: wavelength
d: trough
e: wavelength
f: Longitudinal

But e and c are both wavelength, which might be correct, or perhaps e is something else.

Another possibility: in the diagram, e might be the "period", but period is time, not shown. Or "frequency", no.

Perhaps e is the "energy", but energy is not a dimension.

I think it's fine.

For the longitudinal wave diagram, since it's f. ______ Wave, and we put "Longitudinal", that makes sense.

So I'll go with that.

Final Answer:

1. Energy
2. peaks
3. troughs
4. wavelength
5. amplitude
6. frequency
7. hertz
8. Longitudinal
9. sound
10. transverse

Diagram labels:
a: peak
b: amplitude
c: wavelength
d: trough
e: wavelength
f: Longitudinal

But to be precise, for e, in some interpretations, e might be the equilibrium position, but since it's not in the word bank, and the instruction is to use the word bank for sentences, but for labeling, it might be different. However, the problem says "Complete each sentence below with a word from the word bank. Then label each diagram." so for labeling, we may not be restricted to the word bank, but typically we use the same terms.

Perhaps for e, it's "rest position", but not in bank. I think "wavelength" is acceptable.

Another idea: in the diagram, e is the arrow indicating the wavelength, so it's labeling the wavelength, so "wavelength" is correct.

Similarly, c is also labeling wavelength, so both c and e are wavelength.

Ok.

So final answer as above.