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Fundamental frequency of sonometer wire is n if the length tension and diameter of wire are tripled then the new fundamental frequency is (1)n/root3 (2)n/3 (3)nroot3 (4)n/3root3?
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Fundamental frequency of sonometer wire is n if the length tension and...
Fundamental frequency of sonometer wire of length L, tension T and mass per unit length u is,
f = (1/2L)√(T/u)
Let the mass of the wire be m, density d and it's cross sectional area be A. Then m =(AL)d and u = m/L = Ad. Keeping this back into the above equation,
f = (1/2L)√(T/Ad)
T → 3T
L → 3L
A → 3²A = 9A
f → (1/3)(√3/9) f = (1/3√3) f
Community Answer
Fundamental frequency of sonometer wire is n if the length tension and...
Fundamental Frequency and Sonometer Wire

The fundamental frequency of a sonometer wire is the lowest frequency at which the wire can vibrate. It is directly related to the length, tension, and diameter of the wire. Let's analyze the effect of tripling these parameters on the fundamental frequency.

Effect of Tripling Length

When the length of the wire is tripled, the fundamental frequency decreases. This is because the longer wire takes a longer time to complete one full vibration cycle. Mathematically, the fundamental frequency is inversely proportional to the length of the wire.

Effect of Tripling Tension

When the tension in the wire is tripled, the fundamental frequency increases. This is because the higher tension results in a higher restoring force, which allows the wire to vibrate at a higher frequency. Mathematically, the fundamental frequency is directly proportional to the square root of the tension.

Effect of Tripling Diameter

When the diameter of the wire is tripled, the fundamental frequency decreases. This is because the thicker wire is stiffer and has a higher mass per unit length, which decreases its flexibility. Mathematically, the fundamental frequency is inversely proportional to the diameter of the wire.

Overall Effect on Fundamental Frequency

Since the length, tension, and diameter are all tripled, we need to consider the combined effect on the fundamental frequency.

- The length is tripled, which decreases the frequency.
- The tension is tripled, which increases the frequency.
- The diameter is tripled, which decreases the frequency.

Considering these effects, the overall change in the fundamental frequency can be determined.

The new fundamental frequency is given by:

new frequency = (original frequency) x (1/√3) x (1/√3) x (1/3)

Simplifying this expression, we get:

new frequency = (original frequency) / (√3 x √3 x 3)

Therefore, the new fundamental frequency is (1/3√3) times the original frequency.

Hence, the correct answer is option (1) n/√3.
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Attempt All sub parts from each question.Tuning a piano wire: When we hear two frequencies which are very close to each other but not exactly equal then distinct waxing and waning of the intensity of the sound is heard. These are known as beats. The beat frequency is equal to the absolute value of the difference in frequency of the two waves. To tune a piano, a musician takes help of beat frequency. He plucks the string and tap a tuning fork at the same time. If the two sound sources— the piano string and the tuning fork, do not produce identical frequency then the musician hears detectable beats. Musician will then adjust the tension of the piano string and repeat the process until the beats are no longer be heard. Tension of the wire changes the frequency of the wire.As the piano string becomes more in tune with the tuning fork, the beat frequency reduces and approaches 0 Hz. When beats are no longer heard, the piano string is tuned to the tuning fork; i.e. they play the same frequency. The process allows the musician to match the strings' frequencies to the frequencies of a standardized set of tuning forks.Q. A musician while tuning a piano with a standard tuning fork of frequency 256 Hz, initially heard beats of 5 Hz. He then increased the tension and found that the beat disappears. What was the initial frequency of the piano wire?

Attempt All sub parts from each question.Tuning a piano wire: When we hear two frequencies which are very close to each other but not exactly equal then distinct waxing and waning of the intensity of the sound is heard. These are known as beats. The beat frequency is equal to the absolute value of the difference in frequency of the two waves. To tune a piano, a musician takes help of beat frequency. He plucks the string and tap a tuning fork at the same time. If the two sound sources— the piano string and the tuning fork, do not produce identical frequency then the musician hears detectable beats. Musician will then adjust the tension of the piano string and repeat the process until the beats are no longer be heard. Tension of the wire changes the frequency of the wire.As the piano string becomes more in tune with the tuning fork, the beat frequency reduces and approaches 0 Hz. When beats are no longer heard, the piano string is tuned to the tuning fork; i.e. they play the same frequency. The process allows the musician to match the strings' frequencies to the frequencies of a standardized set of tuning forks.Q. A musician while tuning a piano with a standard tuning fork of frequency 256 Hz, hears beats of 5 Hz. What he should do to achieve the tuning?

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Fundamental frequency of sonometer wire is n if the length tension and diameter of wire are tripled then the new fundamental frequency is (1)n/root3 (2)n/3 (3)nroot3 (4)n/3root3?
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