A musician plays a string alongside a 440 Hz reference tone and hears 5 beats per second. Without any additional information, what can she conclude about her string's frequency?
AHer string is vibrating at 5 Hz
BHer string is flat and vibrating at 435 Hz
CHer string is sharp and vibrating at 445 Hz
DHer string differs from 440 Hz by exactly 5 Hz, but whether it is sharp or flat cannot be determined from beats alone
Beat frequency equals |f₁ − f₂|, giving only the magnitude of the frequency difference, not its sign. A beat rate of 5 beats/sec means the string is either 435 Hz or 445 Hz. To determine direction, the musician must adjust the string and observe whether the beat frequency increases (moving away from 440) or decreases (moving toward it). Beats are an error signal, but not a directional one.
Question 2 Multiple Choice
Two tuning forks at 300 Hz and 304 Hz are struck simultaneously. What is the beat frequency, and what pitch does a listener perceive?
ABeat frequency: 4 Hz; perceived pitch: 4 Hz
BBeat frequency: 4 Hz; perceived pitch: 302 Hz
CBeat frequency: 302 Hz; perceived pitch: 4 Hz
DBeat frequency: 604 Hz; perceived pitch: 4 Hz
These are two independent properties of the combined sound. The beat frequency — the rate of amplitude pulsing — equals |f₁ − f₂| = 4 Hz. The perceived pitch corresponds to the average frequency (300 + 304)/2 = 302 Hz. Option A confuses beat frequency for pitch, which would place the sound nearly below the threshold of hearing as a tone — absurd for a 300 Hz source.
Question 3 True / False
When two tuning forks of slightly different frequencies are struck together, the resulting beat is a new, separate frequency produced by their interaction.
TTrue
FFalse
Answer: False
Beats are not a new frequency — they are an amplitude modulation caused by wave interference. The two original frequencies remain present; they periodically come into phase (reinforcing to produce a loud burst) and out of phase (canceling to produce quiet). No new sound source is created. The brain perceives the pulsing rhythm of beats, but this pulsing is a fluctuation in amplitude of the existing frequencies, not an additional frequency.
Question 4 True / False
As the frequency difference between two waves increases, the beat frequency increases and the amplitude pulsing becomes more rapid.
TTrue
FFalse
Answer: True
f_beat = |f₁ − f₂|, so beat frequency is directly proportional to the frequency difference. A larger gap means the faster wave laps the slower one more often per second, producing more rapid pulsing. This is why instruments that are badly out of tune produce fast, agitated beats, while instruments approaching unison produce slower, smoother beats that eventually disappear.
Question 5 Short Answer
Why does the beat frequency approach zero as two instruments are brought into tune with each other? Explain in terms of the physical process producing beats.
Think about your answer, then reveal below.
Model answer: Beats arise because two waves of slightly different frequencies periodically drift in and out of phase. The beat frequency equals |f₁ − f₂|, measuring how often the faster wave completes one full extra cycle relative to the slower one. As the two frequencies converge, this rate decreases — the waves stay in phase for longer stretches before drifting out of alignment. At zero frequency difference, the waves maintain a constant phase relationship indefinitely, producing no amplitude pulsing at all.
This is why a musician can use beats to tune: the decreasing beat frequency provides continuous audible feedback that the frequencies are converging. When beats disappear completely, the frequencies are identical. Beat detection extends the ear's resolution well below its normal frequency discrimination threshold.