Question:
In Sonometer experiment, the frequency of a tuning fork used is 288 Hz. Harmonics will 'NOT' be produced at the frequency ______.
In Sonometer experiment, the frequency of a tuning fork used is 288 Hz. Harmonics will 'NOT' be produced at the frequency ______.
Show Hint
Harmonics MUST be exact integer multiples of the fundamental frequency ($f_m = m \cdot f_1$). Simply divide the given options by the fundamental to spot the fraction!
Updated On: Jun 19, 2026
- 288 Hz
- 576 Hz
- 844 Hz
- 864 Hz
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
A sonometer wire vibrates in resonance with a tuning fork. We need to determine which frequency is NOT a valid harmonic of the fundamental frequency produced by the tuning fork.
Step 2: Detailed Explanation:
When a sonometer wire is plucked or made to vibrate in resonance, its fundamental frequency ($n$) matches the frequency of the tuning fork.
Here, the fundamental frequency $n = 288$ Hz.
A stretched string fixed at both ends (like a sonometer wire) is capable of producing ALL integer harmonics of its fundamental frequency.
The allowed frequencies are: $n, 2n, 3n, 4n, \dots$
Let's calculate the first few expected harmonics:
- 1st harmonic (Fundamental) = $1 \times 288 = 288$ Hz (Option a is valid)
- 2nd harmonic = $2 \times 288 = 576$ Hz (Option b is valid)
- 3rd harmonic = $3 \times 288 = 864$ Hz (Option d is valid)
- 4th harmonic = $4 \times 288 = 1152$ Hz
Let's look at the remaining option, 844 Hz.
$844 / 288 \approx 2.93$. Because this is not a perfect whole integer, 844 Hz cannot physically be produced as a standing wave (harmonic) on this specific wire.
Step 3: Final Answer:
Harmonics will NOT be produced at 844 Hz, matching option (c).
A sonometer wire vibrates in resonance with a tuning fork. We need to determine which frequency is NOT a valid harmonic of the fundamental frequency produced by the tuning fork.
Step 2: Detailed Explanation:
When a sonometer wire is plucked or made to vibrate in resonance, its fundamental frequency ($n$) matches the frequency of the tuning fork.
Here, the fundamental frequency $n = 288$ Hz.
A stretched string fixed at both ends (like a sonometer wire) is capable of producing ALL integer harmonics of its fundamental frequency.
The allowed frequencies are: $n, 2n, 3n, 4n, \dots$
Let's calculate the first few expected harmonics:
- 1st harmonic (Fundamental) = $1 \times 288 = 288$ Hz (Option a is valid)
- 2nd harmonic = $2 \times 288 = 576$ Hz (Option b is valid)
- 3rd harmonic = $3 \times 288 = 864$ Hz (Option d is valid)
- 4th harmonic = $4 \times 288 = 1152$ Hz
Let's look at the remaining option, 844 Hz.
$844 / 288 \approx 2.93$. Because this is not a perfect whole integer, 844 Hz cannot physically be produced as a standing wave (harmonic) on this specific wire.
Step 3: Final Answer:
Harmonics will NOT be produced at 844 Hz, matching option (c).
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