Transverse Waves Worksheet - Varga-Sturgis - home Pages 1-5 - Flip ... - Free Printable

Let’s solve each part of the worksheet step by step.

---

1. Draw a transverse wave on the next page.

Since we can’t draw here, I’ll describe how to draw it:

- Start with a straight horizontal line (this is the rest position or equilibrium).
- Above and below that line, draw a smooth up-and-down curve — like a sine wave.
- Make sure it goes up, then down through the middle, then down further, then back up through the middle, and repeats.
- Label the highest point as “crest” and the lowest as “trough”.
- You can draw 2 or 3 full waves to show the pattern.

*(Note: Since this is text-based, you’ll need to sketch this on your paper.)*

---

2. Label the crest, trough, wavelength, amplitude in any two positions shown.

Again, since we’re not drawing, here’s what to label on your drawn wave:

- Crest: The very top of a wave bump.
- Trough: The very bottom of a wave dip.
- Wavelength: Measure from one crest to the next crest (or one trough to the next trough) — that’s one full wave length.
- Amplitude: Measure from the middle line (rest position) up to a crest (or down to a trough). That’s how tall the wave is.

Do this for at least two different crests/troughs on your drawing.

---

3. Frequency is the number of complete waves or cycles that happen each second. Write the formula.

The formula for frequency is:

> Frequency = Number of Waves / Time (in seconds)

Or written with symbols:

> f = n / t

Where:
- f = frequency (measured in Hertz, Hz)
- n = number of complete waves
- t = time in seconds

---

4. Frequency is measured in what unit?

Frequency is measured in Hertz, abbreviated as Hz.

One Hertz means one wave per second.

---

5. The frequency of the wave below is [image shows 3 waves over 6 seconds]. How many complete waves will there be every second?

Looking at the graph description (even though we can’t see it, the problem says: “Use the example above to find the frequency...”)

From question 5’s context:
It says “the frequency of the wave below is ___”, and then asks “How many complete waves will there be every second?”

But actually, looking at the graph described later (question 6), it says:

> “Use the example above to find the frequency of the following wave. One way to do this is to figure out how many complete waves fit in 1 complete wave. Then, divide the amount of time by the number of waves.”

Wait — let’s look at the graph data given in question 6’s image description:

It says:
“Displacement (cm)” vs “Time (seconds)”
And the graph shows 3 complete waves between 0 and 6 seconds.

So if 3 waves happen in 6 seconds, then:

> Frequency = Number of waves / Time
> f = 3 waves / 6 seconds = 0.5 Hz

That means 0.5 waves per second.

But wait — the question says: “How many complete waves will there be every second?”

If frequency is 0.5 Hz, that means half a wave per second — so not even one full wave per second.

But maybe the graph in question 5 is different? Let me re-read.

Actually, in the original worksheet, question 5 probably refers to a specific graph. Since the user didn’t provide the actual image, but in the text under question 6, it describes a graph with 3 waves over 6 seconds — which is likely the same one referenced in question 5.

Alternatively, perhaps question 5 has its own small diagram? But since we don’t have it, and the only numerical info is in question 6’s graph, let’s assume question 5 is referring to that same graph.

Wait — no, let’s read carefully:

In the user’s text, after question 5, it says:

> “Use the example above to find the frequency of the following wave. One way to do this is to figure out how many complete waves fit in 1 complete wave. Then, divide the amount of time by the number of waves.”

This seems misphrased. Probably meant: “figure out how many complete waves fit in the total time shown, then divide number of waves by time.”

And the graph shows 3 waves in 6 seconds → 3/6 = 0.5 Hz.

But question 5 says: “The frequency of the wave below is ___ . How many complete waves will there be every second?”

So if frequency is 0.5 Hz, then answer is 0.5 waves per second.

But that feels odd for a beginner question. Maybe the graph in question 5 is different?

Wait — perhaps in the original worksheet, question 5 has a simple diagram showing, say, 2 waves in 1 second? But since we don’t have it, and the only data provided is in question 6’s graph (3 waves in 6 seconds), I think we must use that.

Alternatively, maybe question 5 is theoretical? No, it says “the wave below”, implying a diagram.

Given the ambiguity, but based on standard worksheets, often question 5 might show a wave with 2 cycles in 1 second → frequency = 2 Hz.

But since the only concrete data is from question 6’s graph (which is described as having 3 waves over 6 seconds), and question 5 comes before it, perhaps they are separate.

Wait — looking again at the user’s input:

After question 5, it says:

> “Use the example above to find the frequency of the following wave. One way to do this is to figure out how many complete waves fit in 1 complete wave. Then, divide the amount of time by the number of waves.”

This sentence is confusing. “Fit in 1 complete wave” doesn’t make sense. Probably a typo. Likely meant: “fit in the total time shown”.

And then it shows a graph with displacement vs time, and labels: from 0 to 6 seconds, and 3 full waves.

So for that graph:

Number of waves = 3
Time = 6 seconds
Frequency = 3 / 6 = 0.5 Hz

So for question 5, if it’s referring to that same graph, then:

Answer: 0.5 complete waves per second

But that seems low. Alternatively, maybe the graph in question 5 is different.

Perhaps in the original worksheet, question 5 has a wave that completes 2 cycles in 1 second? Without the image, it’s hard.

But let’s look at the very end: “Use the example above to find the frequency...” — and “example above” likely refers to the graph just mentioned, which is 3 waves in 6 seconds.

Moreover, in many such worksheets, they start with easy numbers.

Another possibility: maybe “the wave below” in question 5 is a different one, but since no data is given, and the only data is in the graph described later, I think we have to go with 3 waves in 6 seconds.

But let’s check the calculation again.

If 3 waves occur in 6 seconds, then in 1 second, number of waves = 3 ÷ 6 = 0.5

So frequency = 0.5 Hz

Therefore, answer to question 5: 0.5

But the question says “how many complete waves will there be every second?” — and 0.5 is not a complete wave. So perhaps they expect the frequency value, which is 0.5 Hz, meaning half a wave per second.

Maybe the graph is different. Let me imagine a common version: sometimes they show 4 waves in 2 seconds → 2 Hz.

But without the image, I have to rely on the text.

Wait — in the user’s message, after question 5, it says:

> “Use the example above to find the frequency of the following wave. One way to do this is to figure out how many complete waves fit in 1 complete wave. Then, divide the amount of time by the number of waves.”

This is poorly worded. “Fit in 1 complete wave” is nonsense. Probably meant: “count how many complete waves are in the time period shown, then divide that number by the time in seconds.”

And the graph shows from 0 to 6 seconds, and there are 3 full waves (from peak to peak or trough to trough).

So yes, 3 waves / 6 seconds = 0.5 Hz.

So for question 5, if it's the same wave, answer is 0.5.

But perhaps question 5 is separate. Let's read the sequence:

Question 5: "The frequency of the wave below is ___ . How many complete waves will there be every second?"

Then immediately after, it says "Use the example above..." — which suggests that "the wave below" in Q5 is the one being referred to in the instruction.

And the instruction mentions a graph with time axis up to 6 seconds and 3 waves.

So I think it's safe to assume that for Q5, the wave has 3 waves in 6 seconds.

Thus, frequency = 3/6 = 0.5 Hz, so 0.5 complete waves per second.

But to confirm, let's do question 6 as well, since it uses the same graph.

---

6. Use the example above to find the frequency of the following wave. ... Then, divide the amount of time by the number of waves.

Wait, it says: “divide the amount of time by the number of waves” — that would give time per wave, which is period, not frequency.

That must be a mistake.

Correct formula: Frequency = Number of waves / Time

Period = Time / Number of waves

So if they say “divide the amount of time by the number of waves”, that gives period.

But the question asks for frequency.

Probably a typo in the worksheet.

In the graph: 3 waves in 6 seconds.

So frequency f = number of waves / time = 3 / 6 = 0.5 Hz

Period T = time / number of waves = 6 / 3 = 2 seconds per wave

But the question asks for frequency, so it should be 0.5 Hz.

However, the instruction says: “divide the amount of time by the number of waves” — which would be 6/3=2, but that’s period, not frequency.

This is confusing.

Perhaps “the example above” refers to something else.

Maybe in the worksheet, there is an example before this that shows how to calculate.

But since we don't have it, and based on standard knowledge, frequency is waves per second.

For the graph described: 3 waves in 6 seconds → frequency = 0.5 Hz.

So for both Q5 and Q6, if they refer to the same graph, answer is 0.5 Hz.

But let's double-check with logic.

If a wave has a frequency of 0.5 Hz, it means it takes 2 seconds to complete one full cycle. In 6 seconds, it completes 3 cycles — which matches.

So yes.

Now, for Q5: “How many complete waves will there be every second?” — answer is 0.5, but since it's "complete waves", and 0.5 is not complete, perhaps they want the frequency value, which is 0.5, implying half a wave per second.

In physics, we say the frequency is 0.5 Hz, meaning 0.5 cycles per second.

So I think it's acceptable.

Perhaps the graph in Q5 is different. Another common setup: sometimes they show a wave with 2 cycles in 1 second, so frequency 2 Hz.

But without the image, and given the data in Q6's description, I'll go with 0.5 for both.

Wait, let's look back at the user's input:

After Q5, it says: "Use the example above to find the frequency of the following wave." — and then describes a graph with 3 waves over 6 seconds.

So "the following wave" is the one in the graph, and "example above" might refer to a previous example, but since none is given, perhaps "example above" is the method.

The method says: "figure out how many complete waves fit in 1 complete wave" — that must be a error. Likely: "fit in the time interval shown".

Then "divide the amount of time by the number of waves" — again, that's for period.

I think there's a mistake in the worksheet's wording.

To resolve this, let's assume that for the graph with 3 waves in 6 seconds:

- Number of waves = 3
- Time = 6 s
- Frequency = 3 / 6 = 0.5 Hz

So for Q5, if it's the same wave, answer is 0.5

For Q6, same thing.

But Q5 says "the wave below", and Q6 says "the following wave", so perhaps they are the same.

Maybe Q5 has a different wave. Let's see the structure.

Perhaps in the original, Q5 has a simple diagram with, say, 1 wave in 1 second, but since not specified, and the only data is from the graph in Q6, I think we have to use that.

Another idea: in some worksheets, "the wave below" for Q5 might be a static diagram with labels, not a time graph, but that doesn't make sense for frequency.

Frequency requires time information.

So likely, Q5 refers to a time-domain graph.

Given all this, I'll proceed with the data from the graph described: 3 waves in 6 seconds.

So frequency = 0.5 Hz.

Therefore:

For Q5: The frequency is 0.5 Hz, so there are 0.5 complete waves every second.

For Q6: Same calculation, frequency = 0.5 Hz.

But let's write the answers clearly.

First, for Q3 and Q4, we have clear answers.

Q3: Formula: frequency = number of waves / time

Q4: Unit: Hertz (Hz)

Q5: Based on graph (assumed 3 waves in 6 seconds): frequency = 3/6 = 0.5 Hz, so 0.5 complete waves per second.

Q6: Same as Q5, since same graph: 0.5 Hz.

But the instruction in Q6 says "divide the amount of time by the number of waves", which would be 6/3=2, but that's incorrect for frequency.

Perhaps "the example above" is a different example.

Maybe "example above" refers to a sample calculation where they did it correctly.

To avoid confusion, let's calculate properly.

Standard definition: frequency f = number of oscillations / time

For the graph: from t=0 to t=6s, there are 3 full cycles (e.g., from crest to crest three times).

So f = 3 / 6 = 0.5 Hz

So answer is 0.5

Now, for the final answer, since the user might expect numerical answers for Q5 and Q6, and the others are descriptive.

But the worksheet has multiple parts.

Perhaps the "Final Answer" should include all parts.

But typically, for such worksheets, the numerical answers are for Q5 and Q6.

Let's list all answers:

1. [Drawn on paper]

2. [Labeled on drawing]

3. Frequency = number of waves / time

4. Hertz (Hz)

5. 0.5

6. 0.5

But for Q5, it says "how many complete waves will there be every second?" — and 0.5 is not a complete wave, so perhaps they want the frequency value, which is 0.5, and it's understood as 0.5 cycles per second.

In some contexts, they might expect "0.5" or "1/2".

Perhaps the graph is different. Let's think of a common problem: if a wave has a period of 2 seconds, frequency is 0.5 Hz.

Yes.

Another possibility: in the graph, if it's from 0 to 6 seconds, and there are 3 waves, but perhaps they mean from start to end, and if it starts at zero and ends at zero after 3 waves, yes.

I think it's correct.

So I'll go with that.

Final Answers:

For Q3: f = n / t or frequency = number of waves / time

For Q4: Hertz or Hz

For Q5: 0.5

For Q6: 0.5

But to box the final answer, perhaps for the numerical parts.

Since the user said "solve the problem accurately", and the problem has multiple parts, I'll provide all.

But in the response format, "Final Answer" should be the concise answer.

Perhaps for this worksheet, the key numerical answers are for Q5 and Q6.

Let's see the user's request: "Solve the problem accurately." and "provide the final correct answer".

Since it's a worksheet, maybe list the answers for each numbered question.

But to follow the format, I'll put the numerical answers in Final Answer.

Alternatively, since Q1 and Q2 are drawings, and Q3 and Q4 are definitions, Q5 and Q6 are calculations.

So for Final Answer, I'll put the values for Q5 and Q6.

But Q5 has two parts: "the frequency is ___" and "how many complete waves every second?" — which is the same thing.

So frequency = 0.5 Hz, and waves per second = 0.5.

Similarly for Q6.

So I think:

Final Answer for Q5: 0.5

Final Answer for Q6: 0.5

But to be precise, let's write it as:

After careful consideration, based on the graph described (3 complete waves in 6 seconds):

- Frequency = number of waves / time = 3 / 6 = 0.5 Hz

So for both Q5 and Q6, the frequency is 0.5 Hz, meaning 0.5 complete waves per second.

Therefore, the answers are:

Q3: frequency = number of waves / time

Q4: Hertz (Hz)

Q5: 0.5

Q6: 0.5

For the Final Answer section, since it's likely expecting the numerical results, I'll box 0.5 for both, but perhaps specify.

Since the user might have a specific expectation, and to keep it simple, I'll provide the answers as per the worksheet.

Another thought: in some versions of this worksheet, the graph for Q5 might show 2 waves in 1 second, but since not specified, and the only data is from the later graph, I'll stick with 0.5.

Perhaps "the wave below" in Q5 is the one in the diagram that is not described, but in the text, after Q5, it refers to "the following wave" which is described.

I think it's consistent.

So let's finalize.

For Q5: The frequency is 0.5 Hz, so there are 0.5 complete waves every second.

For Q6: Using the graph, frequency = 3 waves / 6 seconds = 0.5 Hz.

So the numerical answer is 0.5 for both.

Now for the response.

Since ExplainAnswer is false, etc., I'll just provide the Final Answer after reasoning.

But in the reasoning, I've done it.

So for the Final Answer, I'll put the key numerical answers.

Perhaps:

Final Answer:
For question 5: 0.5
For question 6: 0.5

But to make it clean.

Since the worksheet might expect the frequency value, and for Q5 it's "the frequency is ___", so 0.5, and for Q6, "find the frequency", so 0.5.

Also, for Q3 and Q4, they are not numerical, so perhaps not included in "Final Answer".

I think that's reasonable.

So I'll go with that.