Transverse V Longitudinal Wave Worksheet 2b107dk | PDF | Waves ... - Free Printable

Here are the answers to the worksheet questions, worked out step-by-step.

Step-by-Step Solution

1. Wave Illustrations (P, Q, R, S, T)
* (a) Compare waves P and Q. They both have the same height from the center line (amplitude). However, wave P has peaks that are closer together than wave Q, meaning it repeats more often. This means P has a higher frequency.
* *Result:* Waves P and Q have the same amplitude, but wave P has twice the frequency of wave Q.
* (b) Compare waves Q and R. The distance between their peaks (wavelength/frequency) looks about the same. However, wave Q is tall, and wave R is short. Wave R's height is half of wave Q's.
* *Result:* Waves Q and R have the same frequency (or wavelength), but wave R has twice the wavelength? No, wait. Let's look at the shape. Actually, looking closely at Q and R: Q has 4 cycles. R has 2 cycles in the same space? No, let's count peaks.
* Wave Q: ~4 full waves.
* Wave R: ~2 full waves.
* So Q has twice the frequency of R. Or R has twice the wavelength of Q.
* Let's re-read the prompt for (b): "Waves Q and R have the same \_\_\_\_\_\_, but wave R has twice the \_\_\_\_\_\_ of wave Q."
* Let's look at Amplitude. Q is tall. R is short. Not the same.
* Let's look at Frequency/Wavelength. Q is squished (high freq). R is stretched (low freq). Not the same.
* *Correction*: Let me look at the image again very carefully.
* Wave P: High Amp, High Freq.
* Wave Q: High Amp, Low Freq (relative to P).
* Wave R: Low Amp, Low Freq (same spacing as Q).
* Wave S: High Amp, Changing Freq.
* Wave T: Low Amp, Changing Freq.
* Okay, comparing Q and R again. They have the same horizontal spacing between peaks. That means they have the same frequency (and wavelength). Wave Q is tall, Wave R is short. The prompt says "Wave R has twice the...". Wait, R is smaller than Q. So R cannot have "twice" the amplitude of Q.
* Let's flip it. Maybe the question implies Q has twice the amplitude of R? "Wave R has twice the [wavelength] of wave Q"? No, spacing is the same.
* Let's look at P and Q again for (a). P has tighter spacing. Same height. So Same Amplitude, Twice Frequency. Correct.
* Let's look at Q and R again for (b). Same spacing. Different height. Q is roughly double the height of R. So they have the same frequency. But the sentence says "Wave R has twice the...". This phrasing is tricky if R is the smaller one. Is it possible R has twice the *period*? No, period is inverse of frequency. If freq is same, period is same.
* Let's look really closely at R vs Q.
* Q: 4 humps.
* R: 2 humps.
* Ah! I miscounted initially. In the box provided, Wave Q completes about 4 cycles. Wave R completes only 2 cycles. Therefore, they do NOT have the same frequency.
* Do they have the same amplitude? No, Q is taller.
* Let's re-evaluate (a). P has ~8 cycles. Q has ~4 cycles. Same height. So P has twice the frequency of Q. This holds up.
* Let's re-evaluate (b). "Waves Q and R have the same...". What is the same? Nothing obvious visually except they are both sine waves.
* Let's look at Amplitude. Q is high. R is low.
* Let's look at Wavelength. Q is short wavelength. R is long wavelength.
* Is it possible the question meant "Waves P and S"? No, it says Q and R.
* Let's look at the blank structure: "Wave R has twice the [BLANK] of wave Q." Since R is "stretched out" compared to Q, R has a longer wavelength. Specifically, since Q has 4 waves and R has 2 waves in the same space, R's wavelength is twice as long as Q's.
* So what do they have the "same" of? They don't have the same amplitude. They don't have the same frequency.
* Maybe the question refers to speed? If these are on the same string/medium, speed is constant. But usually, these diagrams test visual properties.
* Let's look at another possibility. Did I misidentify Q and R?
* P: High Amp, Short Lambda.
* Q: High Amp, Medium Lambda.
* R: Low Amp, Long Lambda.
* S: High Amp, Varying Lambda.
* T: Low Amp, Varying Lambda.
* There might be a typo in the question or my interpretation of "Same". Let's look at Q and T? No.
* Let's look at P and S? No.
* Let's reconsider Q and R. Is it possible they have the same energy? No.
* Let's assume the question meant "Waves Q and P have the same amplitude..." (Done in A).
* Let's look at R and T? T varies.
* Let's look at Q and S? S varies.
* Actually, let's look at the heights again. Q is tall. R is short.
* Let's look at the widths. Q is narrow. R is wide.
* There is no property that is the "same" between Q and R visually.
* *Alternative interpretation*: Maybe "Waves Q and R have the same wave type"? Unlikely.
* Let's look at question (e): "Waves \_\_\_ and \_\_\_ have a low amplitude and a steady frequency." That would be R and... wait, T changes frequency. So just R? Or maybe Q and P are "High", R is "Low". Who else is low and steady? None of the others are steady.
* Let's re-read (b) carefully. "Waves Q and R have the same \_\_\_\_\_\_".
* Could it be phase? No.
* Could it be that I am misseeing the image? Let's assume standard physics problem patterns. Usually, you compare two variables: Amp and Freq.
* Pair 1 (P & Q): Same Amp, Diff Freq.
* Pair 2 (Q & R): Diff Amp, Diff Freq. This is a bad pair for comparison unless one variable is held constant.
* Is it possible R has the same Amplitude as... T? No, T varies.
* Is it possible Q has the same Frequency as... P? No.
* Let's look at R and Q again.
* Maybe the question meant Waves P and S? Same Amplitude.
* Maybe the question meant Waves Q and S? Same Amplitude.
* Let's assume there is a typo in the book and it meant Waves Q and S have the same amplitude, but wave S has changing frequency? No, the second part says "Wave R has twice the...".
* Let's try this: Maybe R has twice the Period of Q? Period is time per cycle. If R is half the frequency, it has twice the period. And do they have the same "Speed"? If they travel in the same medium, yes.
* *Most likely intended answer for a middle-school level*: The question might contain a typo for "Waves Q and P" or similar. BUT, looking at Q and R, if we must fill it:
* They definitely don't have the same amplitude.
* They definitely don't have the same frequency.
* However, if we look at Wave Q and Wave R, and we assume the medium is the same, they have the same speed. And since $v = f \lambda$, if $v$ is constant, and $f_Q = 2 f_R$, then $\lambda_R = 2 \lambda_Q$.
* So: Waves Q and R have the same speed, but wave R has twice the wavelength of wave Q. (This assumes knowledge that wave speed depends on the medium, not the source).

* (c) "Steady frequency but changing amplitude."
* Steady frequency means the horizontal spacing between peaks stays consistent.
* Changing amplitude means the height goes up and down.
* Looking at the images: S has consistent spacing (mostly) but the height gets big and small. Wait, S looks like the spacing changes too? Let's look at T. T has low height, but spacing changes.
* Let's look at S again. The peaks are fairly evenly spaced, but the envelope (height) grows and shrinks. This is amplitude modulation.
* Let's look at T. The height is low, but the peaks get closer and further apart. This is frequency modulation.
* So, S shows steady frequency (approx) but changing amplitude.

* (d) "Steady amplitude but changing frequency."
* Steady amplitude means the height stays the same.
* Changing frequency means the peaks get squished and stretched.
* Looking at T: The height is consistently low. The spacing between peaks changes (wide, then narrow, then wide).
* So, T shows steady amplitude but changing frequency.

* (e) "Low amplitude and a steady frequency."
* Low amplitude: Shorter waves. Candidates: R, T.
* Steady frequency: Even spacing. Candidates: P, Q, R.
* Intersection: R.
* Is there another one? T has changing frequency. P and Q have high amplitude.
* Wait, is T considered "steady frequency"? No, it clearly chirps.
* Is there a wave I missed? No.
* Maybe Q is considered "low" compared to P? No, P and Q are same height.
* Maybe the question implies R and... ?
* Let's look at T again. Is the amplitude steady? Yes. Is the frequency steady? No.
* Let's look at S. Amplitude changes.
* Perhaps the answer is just R? But there are two blanks: "Waves \_\_\_ and \_\_\_".
* Let's re-examine T. Does it have a steady frequency? The middle part is squished, ends are wide. No.
* Let's re-examine R. Low amp, steady freq.
* Let's re-examine Q. High amp.
* Let's re-examine P. High amp.
* Is it possible T is considered low amplitude and the frequency change is ignored? Unlikely.
* Is it possible S is considered low amplitude? No, it gets very high.
* Maybe I should look at Q and R again. If Q is "Medium" and R is "Low"?
* Let's look at the diagram labels again. P, Q, R, S, T.
* Maybe the second wave is T despite the frequency change? Or maybe S?
* Actually, look at T's amplitude. It is low. Look at R's amplitude. It is low.
* Look at T's frequency. It varies.
* Look at R's frequency. It is steady.
* There is only one wave with Low Amp AND Steady Freq: R.
* Could the other one be Q if we consider P "Very High"? No, P and Q are drawn with same peak height.
* Let's assume the question considers T to have a "steady average frequency" or it's a trick question?
* Or perhaps S and T are the "changing" ones, and P, Q, R are the "steady" ones. Among P, Q, R, which are low amplitude? Only R.
* Let's look at the blanks again. "Waves \_\_\_\_ and \_\_\_\_".
* Is it possible Q is considered low amplitude relative to S?
* Let's guess the intended answer is R and T (focusing on amplitude being low, ignoring the freq change in T for a moment? No, that's bad physics).
* Let's look at P and Q. Same Amp.
* Let's look at R. Low Amp.
* Let's look at T. Low Amp.
* If forced to pick two "Low Amplitude" waves, it is R and T. Even though T's frequency changes, it is the only other "Low" one.
* *Self-Correction*: Look at wave T again. The amplitude is small and constant. The frequency changes.
* Look at wave R. The amplitude is small and constant. The frequency is constant.
* Look at wave Q. Amplitude is large.
* Look at wave P. Amplitude is large.
* Look at wave S. Amplitude changes.
* There is strictly only one wave with Low Amp + Steady Freq.
* However, sometimes in these worksheets, Q might be considered "lower" than P/S? No.
* Let's assume the question asks for "Low Amplitude" (R and T) and "Steady Frequency" (P, Q, R). The intersection is R.
* Maybe the second blank is for a wave that *doesn't exist*? No.
* Let's look at T again. Is the frequency actually steady? Left side: wide. Middle: narrow. Right side: wide. Definitely not steady.
* Let's look at S. Left: narrow. Middle: wide. Right: narrow.
* Okay, I will provide R as the primary answer. If a second is absolutely required by the format, T is the only other low-amplitude wave, but it fails the frequency test.
* *Wait*, look at Q and R in question (b) again. If Q and R had the same frequency, R would have to be stretched horizontally to match Q's peaks. It isn't.
* Let's go with the most distinct features.
* (a) P & Q: Same Amplitude, P has twice Frequency.
* (b) Q & R: This is the problematic one. Let's look at P and R. P has 8 cycles, R has 2. P has 4x freq.
* Let's look at Q and T. Q has 4 cycles. T has ~5-6 varying cycles.
* Let's assume the question (b) has a typo and meant Waves P and Q have the same amplitude... wait that's (a).
* What if (b) is Waves S and T? Same... nothing.
* What if (b) is Waves Q and S? Same Amplitude. But S doesn't have "twice the [something]" of Q in a simple way.
* Let's stick to the Speed/Wavelength logic for (b) as it's the only physically sound deduction for "Twice". $f_Q \approx 2 f_R \rightarrow \lambda_R = 2 \lambda_Q$. Same Speed.

* (c) Steady Freq, Changing Amp: S.
* (d) Steady Amp, Changing Freq: T.
* (e) Low Amp, Steady Freq: R. (If a second is needed, it's likely an error in the question, but T is low amp). I will list R and note T is low amp but changing freq. Actually, looking at typical answer keys for this specific worksheet online: The answer is often just R. But there are two blanks. Let's look at Q again. Is it possible Q is "Low" compared to S? No.
* Let's try R and T? No.
* How about Q and R have the same Speed? Yes.
* Let's leave (e) as R and potentially none or T (with caveat). I'll provide R as the clear winner. If I must fill two, I'll check if Q is considered "medium" and R "low".
* Actually, let's look at P and Q. P is high freq. Q is low freq.
* Let's look at R. Low freq.
* Maybe Q and R are both "Low Frequency" compared to P? And R and T are "Low Amplitude"?
* Question (e) asks for Low Amp AND Steady Freq.
* Only R fits perfectly. I will write R. If the student needs two, they might accept T loosely, but it's incorrect. I will provide R as the main answer.

2. Diagram Questions
* (a) The wave shows coils moving back and forth along the direction of the spring. This is a longitudinal wave.
* (b) Letter H points to the area where coils are bunched together. This is a compression. Letter I points to the area where coils are spread apart. This is a rarefaction.
* (c) Letter G measures the distance from one compression to the next compression. This is one wavelength.

3. Swing Frequency
* Formula: Frequency = Number of Cycles / Time.
* Cycles = 6 swings.
* Time = 30 seconds.
* Calculation: $6 / 30 = 1 / 5 = 0.2$.
* Unit: Hertz (Hz) or swings per second.
* Answer: 0.2 Hz.

4. Perpendicular Vibration
* Definition: A wave where particles move perpendicular (at right angles) to the direction the wave travels is a transverse wave.

5. Parallel Vibration
* Definition: A wave where particles vibrate parallel (along the same line) to the direction of travel is a longitudinal wave.

6. Compressions and Rarefactions
* These features are characteristic of longitudinal waves (like sound or springs).

7. Horizontal Spring Up and Down
* Moving a spring up and down creates peaks and troughs moving sideways. The vibration (up/down) is perpendicular to travel (sideways). This produces a transverse wave.

8. Wave with a Wavelength
* Trick question? All periodic waves have a wavelength. Both transverse and longitudinal waves have wavelengths.
* Answer: All waves (or both Transverse and Longitudinal).

9. Measure Wavelength
* Since I cannot physically use a ruler on your screen, I will explain how to do it.
* Identify two identical points on adjacent waves (e.g., top of one curve to top of the next curve).
* Place the ruler's zero mark on the first peak.
* Read the measurement at the next peak.
* *Estimation based on standard print size*: Usually, these diagrams are printed such that the wavelength is a whole number like 2 cm or 3 cm. Without the physical paper, I cannot give the exact number. I will instruct the student to measure from crest to crest.

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Final Answer:

1. Wave Illustrations
(a) Waves P and Q have the same amplitude, but wave P has twice the frequency of wave Q.
(b) Waves Q and R have the same speed (assuming same medium), but wave R has twice the wavelength of wave Q. *(Note: Visually, R is stretched out twice as much as Q).*
(c) Wave S shows a steady frequency but changing amplitude.
(d) Wave T shows steady amplitude but a changing frequency.
(e) Waves R (and potentially T if ignoring frequency change) have a low amplitude. *Strictly speaking, only R has both low amplitude and steady frequency.*

2. Diagram Questions
(a) Longitudinal
(b) Letter H represents a compression and letter I represents a rarefaction.
(c) Letter G represents a wavelength.

3. Swing Frequency
The frequency is 0.2 Hz (or 0.2 swings per second).
*(Calculation: 6 swings ÷ 30 seconds = 0.2)*

4. Perpendicular Vibration
Transverse wave.

5. Parallel Vibration
Longitudinal wave.

6. Compressions and Rarefactions
Longitudinal wave.

7. Spring Up and Down
Transverse wave.

8. Wave with a Wavelength
All waves (Both transverse and longitudinal waves have wavelengths).

9. Measure Wavelength
*Action Required:* Place your ruler on the paper. Measure the distance from the top of one coil loop to the top of the very next coil loop. That distance in centimeters is your wavelength.