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Physics Chapter 9 : Topic 15
Beats in Musical Instruments
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Two tuning forks produce frequencies of $\mathbf{256\ Hz}$ and $\mathbf{260\ Hz}$ when sounded together. The listener will hear beats of frequency:
Reasoning: Beat frequency is the difference between two frequencies:$\mathbf{f}_{\mathbf{b}}\mathbf{=}\left| \mathbf{f}_{\mathbf{1}}\mathbf{-}\mathbf{f}_{\mathbf{2}} \right|\mathbf{=}\left| \mathbf{260 - 256} \right|\mathbf{= 4\ Hz}$
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A musician hears a regular rise and fall in loudness when two notes are played together. This phenomenon is due to:
Reasoning: Beats occur due to periodic constructive and destructive interference between two sound waves having slightly different frequencies.
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A guitarist tunes a string by comparing its sound with a reference note. When the beats disappear, it indicates that:
Reasoning: No beats means beat frequency is zero, which occurs when the two frequencies are identical.
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A violin string and a tuning fork produce $\mathbf{5}$ beats per second. If the tuning fork frequency is $\mathbf{440\ Hz\ }$, the violin string frequency could be:
Reasoning: Beat frequency is the absolute difference: $\left| \mathbf{f}_{\mathbf{1}}\mathbf{-}\mathbf{f}_{\mathbf{2}} \right|\mathbf{= 5}$So, the violin frequency can be $\mathbf{440 + 5\ \ }$or $\mathbf{440 - 5}$.
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In a piano, beats may be produced when:
Reasoning: Piano strings can create beats when their frequencies are slightly different, causing alternating loud and soft sounds.
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A musician adjusts a guitar string and notices that the beat frequency decreases. This means:
Reasoning: Beat frequency depends on frequency difference. A decrease in beats means the frequencies are becoming closer.
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Which musical instrument commonly uses the phenomenon of beats for tuning?
Reasoning: String instruments like guitar, violin, and piano use beats between notes to achieve proper tuning.
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Two organ pipes produce frequencies of $\mathbf{300\ Hz}$ and $\mathbf{304\ Hz}$. The number of beats heard in one second is:
Reasoning: $\mathbf{f}_{\mathbf{b}}\mathbf{= |304 - 300| = 4\ Hz}$Therefore, four beats occur per second.
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The main purpose of producing beats in musical instruments is to:
Reasoning: Musicians use beats as a frequency comparison method during tuning.
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A flute player and a violin player produce nearly identical notes. The resulting beats indicate that:
Reasoning: Beats occur only when frequencies are close but not exactly equal.
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When two sound waves produce beats, the loudness becomes minimum when the waves are:
Reasoning: Minimum loudness occurs during destructive interference when waves are out of phase.
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If two notes of frequencies $\mathbf{500\ Hz}$ and $\mathbf{510\ Hz}$ are played together, the listener hears:
Reasoning: Beat frequency: $\mathbf{f}_{\mathbf{b}}\mathbf{= |510 - 500| = 10\ Hz}$
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A piano tuner hears faster beats while adjusting a string. To reduce the beats, he should:
Reasoning: Fewer beats mean a smaller frequency difference, so the frequencies must become closer.
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Two guitar strings produce frequencies of $\mathbf{250\ Hz}$ and $\mathbf{255\ Hz}$. The beat frequency will be:
Reasoning: $\mathbf{f}_{\mathbf{b}}\mathbf{= |255 - 250| = 5\ Hz}$
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The waxing and waning of sound intensity in beats occurs because:
Reasoning: Interference causes periodic changes in resultant amplitude, producing changes in loudness.
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A musician wants to create beats using two tuning forks. Which pair will produce the most noticeable beats?
Reasoning: Beats are clearly heard when frequencies are close together but not identical.
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In a violin, two strings are tuned to almost the same frequency. The sound produced is unpleasant because:
Reasoning: A noticeable frequency difference produces beats that affect sound quality.
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A tuning fork of $\mathbf{512\ Hz}$ produces $\mathbf{6}$ beats per second with a guitar string. Possible frequency of guitar string is:
Reasoning: $\left| \mathbf{f}\mathbf{- 512} \right|\mathbf{= 6}$ $\mathbf{\Longrightarrow}$ $\mathbf{f}\mathbf{= 512 \pm 6}$ $\mathbf{\Longrightarrow}$ giving $\mathbf{506\ Hz\ \ }$or$\ \ \mathbf{518\ Hz}$
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Which condition is necessary for the formation of audible beats?
Reasoning: Audible beats require two waves with slightly different frequencies.
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A drummer and a guitarist play together. No beats are heard between their sounds because:
Reasoning: Beats are heard only when frequencies are nearly equal. Large frequency differences do not produce audible beats.
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A guitar string has frequency $\mathbf{300\ Hz}$. Another string is adjusted from $\mathbf{310\ Hz}$ toward$\mathbf{\ }\mathbf{300\ Hz}$. The beat frequency will:
Reasoning: As the frequency difference decreases, the beat frequency also decreases.
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The frequency of beats produced by two musical notes depends on:
Reasoning: Beat frequency is given by: $\mathbf{f}_{\mathbf{b}}\mathbf{=}\left| \mathbf{f}_{\mathbf{1}}\mathbf{-}\mathbf{f}_{\mathbf{2}} \right|$
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A piano tuner hears one beat every second while comparing a string with a standard note. The frequency difference between them is:
Reasoning: One beat per second means beat frequency is $\mathbf{1\ Hz}$.
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Which statement about beats in musical instruments is correct?
Reasoning: Beats are a result of interference between two sound waves of slightly different frequencies.
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A musician hears $\mathbf{8}$ beats per second between two notes. After adjustment, the beats become $\mathbf{2}$ per second. This shows that:
Reasoning: Beat frequency equals frequency difference. The difference changed from $\mathbf{8\ Hz}$ to $\mathbf{2\ Hz}$, so it decreased by $\mathbf{6\ Hz}$.
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