2: The Source of a Wave Is Moving at 150 Cycles per Second. What Is the Frequency of the Wave It Produces 300 Hz 150 Hz 1 Hz 75 Hz: The Answer Is 150 Hz

The answer is 150 Hz. A wave source vibrating at 150 cycles per second produces a wave whose frequency is exactly 150 Hz, because wave frequency is determined by the source that generates it, not by the speed at which the wave travels through a medium. Among the four options listed, 150 Hz is correct; 300 Hz, 1 Hz, and 75 Hz are all incorrect. That single fact unlocks the rest of the physics involved.

The figure of 150 cycles per second is already stated in hertz by definition. One hertz equals one cycle per second, so 150 cycles per second is simply 150 Hz. Nothing else in the question changes that number. Not the medium, not the wave speed, and not the wavelength. The only thing the source's motion controls is how often a disturbance is launched, and that rate passes straight through to the wave.

This distinction between source frequency and wave speed trips up a lot of students. A common mistake is to think the wave's frequency must be higher because the source is "moving." Movement changes where each cycle starts, not how many cycles leave the source each second. Unless the source is moving relative to an observer in a way that produces a Doppler shift, the frequency reaching a stationary observer stays the same.

The three wrong answers usually come from applying the wrong formula. Doubling 150 gives 300, halving it gives 75, and 1 Hz is a unit confusion. Each of those choices reflects a specific conceptual error worth naming. Below, I work through each one, explain the physics, and give the exact reasoning you need for an exam or a homework set.

What 150 Cycles per Second Actually Means in Hertz

Hertz is the SI unit of frequency, defined as one event per second. A source oscillating 150 times in a single second therefore emits at 150 Hz. The unit conversion is not a calculation; it's a definition. When a textbook writes "150 cycles per second," it has already given you the frequency in hertz.

The confusion often comes from mixing up angular frequency (ω) with ordinary frequency (f). Angular frequency is measured in radians per second and equals 2π times the frequency in hertz. So if a problem gives you ω = 150 rad/s, then f = 150 ÷ (2π) ≈ 23.9 Hz, which is a completely different figure. Make sure your source's "cycles per second" refers to whole cycles, not radians.

A good way to keep this straight: hertz counts oscillations, rad/s counts angle turned. One full oscillation turns 2π radians, so hertz and rad/s differ by a factor of about 6.28. In this problem the wording is "cycles per second," which is the hertz definition, so no division by 2π applies.

Checking units is a habit worth building. Write "150 cycles/second" as "150 × (1/second)" and substitute 1/second = 1 Hz. The unit lands on hertz cleanly with a coefficient of 150. Any answer other than 150 Hz requires an additional operation the problem never asked for. That's the cleanest audit you can run on your own work.

Why the Wave Frequency Always Matches the Source Frequency

When a source completes one oscillation, it launches exactly one wave cycle into the medium. Two oscillations launch two cycles, and 150 oscillations launch 150 cycles every second. The count leaving the source per second is the count arriving at any stationary point per second. No cycles appear or vanish along the way.

Think of a rope tied to a hand shaking up and down. Your hand shakes 150 times a second, so 150 crests travel down the rope each second, regardless of how taut the rope is. If you shake faster, crests get closer together and the frequency rises; the waves also travel to the far end at whatever speed the rope permits. The source sets the frequency; the medium sets the speed.

This is sometimes called the "source rule," and it shows up in every wave type. Sound from a guitar string, light from an LED, water ripples from a dropped stone, seismic waves from a fault slip: each wave's frequency is fixed by the thing that made it. The speeds differ wildly, from roughly 343 m/s for sound in air at room temperature to about 300,000,000 m/s for light in a vacuum, but that speed never rewrites the source's rate.

The deeper reason is energy conservation and continuity. A medium has to keep passing disturbances through its own material; if one end receives 150 pushes a second, the other end passes along 150 pushes a second. A discrepancy would mean waves piling up or disappearing inside the medium, which doesn't happen for a steady traveling wave. For readers who want the formal version, this is the same reasoning that underlies the continuity equation in wave mechanics.

Source Speed Versus Wave Speed: The Difference That Causes Wrong Answers

The phrase "the source is moving" in the question is doing a lot of work, and most wrong answers treat it as if it changed the frequency. In the standard setup, the source moves as it oscillates, but its motion is the mechanism of wave creation, not a distortion of the rate. If the source oscillates at 150 Hz and moves slowly compared to the wave, the emitted frequency is still 150 Hz.

Take an everyday example. A mosquito's wings beat around 400 to 600 times per second, producing its characteristic buzz. A person inside the same room receives about 400 to 600 wave cycles per second, and that's why the pitch stays roughly constant as the mosquito trades positions. The number of pressure oscillations reaching the ear equals the number the wings produced per second. Source and received frequency match.

Different wave speeds do not change this. Sound waves in air at 20 °C travel about 343 m/s, and the same 150 Hz source in seawater, where sound travels about 1,500 m/s, would emit a 150 Hz wave again. The waves would be spaced farther apart in seawater because the speed is higher, but their rate of arrival at a stationary listener would remain 150 per second. Frequency holds steady; only wavelength shifts.

Some readers ask whether "moving at 150 cycles per second" might mean moving 150 meters per second. It doesn't. "Cycles per second" is a count of repetitions, not a distance over time. Read it as a rate of oscillation, and let the wave-speed value be a separate variable, usually something like 340 m/s in physics problems. The frequency answer does not touch that variable at all.

Applying the Wave Equation: Frequency, Wavelength, and Speed Together

The wave equation ties the three quantities together: wave speed equals frequency times wavelength, written in plain text as v = f × λ. Solve for frequency and you get f = v ÷ λ. Both readings give the wavelength for any known speed. That is the only place the frequency value can be turned into a numeric wavelength.

To see the table in action, suppose a problem adds a speed of 340 m/s. Then λ = 340 ÷ 150 = 2.267 m. If a problem instead gives wavelength 2 m and asks for speed, then v = f × λ = 150 × 2 = 300 m/s. Either direction works because the equation is a multiplication identity. Frequency is the anchor and stays at 150 Hz.

Here's a worked audit. The wrong answer choices of 300 Hz and 75 Hz correspond to multiplying frequency by 2 and dividing by 2. Anchored to the table, 300 Hz would need 300 waves launched each second from a source that only cycles 150 times. That is impossible without the source changing. The 75 Hz option would mean half the cycles vanish after leaving the source, which contradicts steady-state wave mechanics.

Remember that wavelength is an output, not an input. Many students reverse the relationship by assuming a given wavelength forces a new frequency. Wavelength follows from the medium's wave speed for the given frequency, never the other way round in a source-driven problem. Keep that direction fixed and the arithmetic stays honest.

The Correct Answer Checked Against the 300 Hz Trap

The 300 Hz choice usually appears because the reader doubles the source rate. Doubling hints at a subharmonic or overtone error, though on a string fixed at both ends, the second harmonic is twice the fundamental frequency. Here, though, the drawn frequency is 150 Hz and nothing produces a harmonic multiple. A 150 Hz source emits a 150 Hz wave, and 300 is simply 2 × 150.

Run a quick check. If a source sent 300 waves per second, it would need to complete 300 oscillations per second, not 150. The problem says the source cycles 150 times each second. To get 300 waves out per second from that source, you would need two wave cycles per oscillation, which no ordinary mechanical source produces. The doubling is a formula slip, likely from confusing f with the doubled frequency in a "second harmonic" setup that never appears in the problem statement.

A common version of this mistake shows up when students read "moving at 150 cycles per second" as a speed. If they think the source is traveling at 150 units per second and the wave leaves at the same speed, they might double to get the relative rate. That assumes two speeds add, which is a Galilean velocity-addition idea. Frequency isn't a speed; frequencies add only via mixing, not by summing as vectors.

The cleanest test is dimensional. Multiplying cycles per second by 2 gives cycles per second doubled, which is a frequency of 300 Hz only if the source actually changed. The problem's boundary is fixed: one source, one motion, one rate. So 300 Hz fails on the source rule. Keep the source rate as the final answer and the doubling disappears.

Why 75 Hz and 1 Hz Fail

The 75 Hz answer cuts the source rate in half. That would correspond to a source emitting only one wave for every two oscillations, or to a medium that absorbs every other cycle. Neither happens here. A source at 150 cycles per second deposits 150 disturbances into the medium every second, so 75 Hz is arithmetically inconsistent with the given figure.

The 1 Hz choice is even easier to dismiss. It treats the number 150 as irrelevant to frequency and converts units incorrectly, perhaps conflating "1 cycle per second" with a single whole cycle per second when the source actually delivers 150. One hertz means one complete oscillation in a second. A source shaking 150 times per second is 150 times faster than a 1 Hz source, not equivalent to it.

None of the distractors uses the actual wave equation. If students write f = v ÷ λ with an assumed speed of 340 m/s and an assumed wavelength, the answer could land anywhere. But the very strength of the question is that the answer does not require an assumption. It sits entirely in the source's oscillation rate. That's a useful exam pattern to notice: sometimes a word problem's extra details are red herrings.

Testing against a second consistent transfer helps. If you measured the frequency at a fixed point near the source, you'd count 150 crests per second. Walk away slowly and the count stays near 150 (the Doppler effect is tiny at walking speed). A 75 Hz outcome would require every other crest to be absorbed or merged, which a linear medium does not do. Physics and arithmetic both point at 150 Hz.

Doppler Shift Only Changes the Observed Frequency When Relative Motion Is Involved

Here's the one scenario where a moving source does produce a different measured frequency: when it moves toward or away from an observer fast enough for the Doppler effect to matter. A source sweeping toward a listener at a fair fraction of the wave speed compresses wavelengths and raises the observed frequency. But that altered frequency is not the same as the frequency of the wave the source produces.

The Doppler formulas make the distinction concrete. For sound in air, the observed frequency is f_observed = f_source × (v ÷ (v − v_source)) for a source approaching a stationary listener, where v is the wave speed. If a 150 Hz siren moves toward a listener at 34.3 m/s (about 10% of 343 m/s), the observed frequency would be 150 × (343 ÷ 308.7) = 150 × 1.111 ≈ 166.7 Hz. The source still generates a 150 Hz wave; the listener hears a stretched version of it.

There's an edge case where even this is small. A source moving toward a listener at about 1.5 m/s (a walking pace) shifts 150 Hz by only about 0.65 Hz, which is harder to hear than a tuning fork's beat. For everyday physics problems where the source motion is gentle or unspecified, the observed frequency essentially equals 150 Hz. The 150 Hz answer stands for the produced wave, and Doppler modifies what an observer records, not the emission rate itself.

Light works the same way with a different formula. A source approaching a stationary observer produces a blueshift, a source receding produces a redshift, and the emitted frequency is fixed by the atomic transition or source process. Astronomers use the redshift to measure galactic recession velocities, and they treat the emitted frequency as a known quantity. This asymmetry between emission and reception is the key contrast to the 300 Hz answer and the physics behind it.

Sound Versus Light: Source Rule Across Different Waves

The rule that wave frequency equals source frequency applies to all wave types, but sound and light supply the two cleanest textbook examples. A tuning fork rated at 440 Hz produces 440 Hz sound whether it's in air, water, or a vacuum, except that a vacuum has no medium for sound. Light from a monochromatic laser produces a single frequency fixed by its emission mechanism regardless of the glass or vacuum it crosses.

Notice how frequency ranges sit far apart from speed ranges. A 150 Hz sound in air and a 150 Hz sound in seawater share a frequency but have wavelengths of about 2.3 m and 10 m. Same source rate, different medium, different spacing. That's the source rule in action and the reason the frequency field of a wave table is filled in first.

What surprises people is how "cycles per second" means the same thing for all of them. The number of times a transducer fires each second, or the number of times a surf board rocks the water, is the frequency delivered to the medium. Crossing glass with light slows it and changes its wavelength but not its frequency. Ask any optics student to compute the frequency of light entering a block of glass and the emitted frequency remains unchanged; that's the standard convention taught in university physics courses.

One practical corner case: software that synthesizes waveforms. A digital oscillator set to 150 Hz produces 150 Hz regardless of the sample rate, as long as the rate is above 300 Hz (the Nyquist limit of twice the frequency). If you downsample to 200 Hz, a 150 Hz tone aliases to 50 Hz. That is a resampling artifact, not a source rule violation; the original source really emitted 150 Hz.

How to Solve Source-Frequency Problems Without Guessing

Use a fixed routine. Read the units, decide whether the figure describes a rate of oscillation or a speed, and write the frequency down before touching any other formula. Then work through the problem in the same order every time. That habit catches the 300 Hz, 75 Hz, and 1 Hz errors before they get marked wrong.

1: Identify the source frequency: if the problem says "cycles per second," write that number in hertz. 2: Note the wave speed if provided: keep it as a separate quantity and don't mix it into the frequency. 3: Use f = v ÷ λ only if wavelength is given, and solve for whichever quantity is missing. 4: Check units on every term: hertz must sit alone in the frequency slot. 5: Do a source-rule audit: does the answer plus the given setup make the source emit the same number of cycles per second it oscillates? If not, something was inverted.

A quick failure case shows why this matters. Suppose a student reads a problem about a bug chirping at 300 Hz in air at 340 m/s and is asked for the wavelength. Applying λ = v ÷ f = 340 ÷ 300 ≈ 1.13 m is correct. The trap is reversing the ratio: f = v × λ = 300 × 340 would be wrong. If the units test says m/s divided by Hz gives metres, you're on track; if they don't reduce correctly, stop and rewrite.

Do this self-audit on the present question and the answer is visible: 150 cycles per second becomes 150 Hz at step one, and none of the later formula operations applies because the problem asks only for frequency. Confirming the answer a second time is possible by asking whether 300, 75, or 1 Hz would require the source's rate to change. Each would, so only 150 Hz survives.

FAQ

What if the source really is moving quickly toward me — does the answer become 300 Hz?

The observed frequency could rise above 150 Hz, but it does not reach 300 Hz at ordinary speeds. For sound in air at 343 m/s, a 150 Hz source would need to approach at 171.5 m/s, half the speed of sound, to double the observed frequency. At that speed the Doppler formula gives 300 Hz, which is a much faster source than a typical "moving" wave source.

Is 150 cycles per second the same as 150 revolutions per minute?

No. One cycle per second equals 60 cycles per minute, so 150 cycles per second equals 9,000 cycles per minute. A motor rated at 150 rpm turns only 2.5 times per second, which would produce a 2.5 Hz wave if it were the source. Always convert the time unit before comparing.

Can wave frequency ever differ from source frequency without Doppler?

Yes, in crystals and nonlinear materials. A nonlinear medium can generate harmonics at 300 Hz, a second harmonic, from a 150 Hz drive, and frequency mixers add or subtract frequencies. For a linear medium and an ordinary source, the source rule holds. It's the linearity plus the source-frequency definition that makes 150 Hz robust.

If wavelength is 1 m and the source is 150 Hz, what is the wave speed?

Speed equals frequency times wavelength: 150 Hz × 1 m = 150 m/s. That's about 44% of the speed of sound in air at room temperature and far below the speed of light. The frequency remains 150 Hz; only the medium's speed determines the wavelength for that source.

How many times does a 150 Hz source oscillate in one minute?

It oscillates 9,000 times in a minute, since 150 per second multiplied by 60 seconds equals 9,000. A wave leaving the source in a steady medium sends out 9,000 cycles over the same minute, so a receiver at rest picks them up at 150 Hz.

Where does the 1 Hz answer usually come from?

Most often it's a unit mistake, confusing a value of 1 (as in one cycle per second) with the actual count of 150. It can also appear when a student divides by an assumed 150-second period. If the problem stated the period as 1 second, the frequency would be 1 Hz, but the given period is 1/150 second.

Does a change in medium temperature change a 150 Hz source's wave frequency?

No for sound emitted by that source. The wave speed in air depends on temperature, rising by about 0.6 m/s per degree Celsius near room temperature. At 15 °C the speed is about 340 m/s; at 20 °C it's about 343 m/s. The wavelength stretches or shrinks with speed, but the frequency stays at 150 Hz.

How do I know 150 Hz is the answer and not 150 divided by 2π?

The denominator 2π applies to angular frequency, measured in radians per second. A figure in "cycles per second" has already given the count of full cycles, and one cycle equals 2π radians. Multiply by 2π to get about 942 rad/s from 150 Hz, or divide by 2π only if you were handed a rad/s value first. For 150 cycles per second, the hertz value is 150 exactly.